The Acropolis Museum opened in Athens last weekend amid controversy that Greek officials did everything possible to stir up. It wasn't enough that, after years of delays, Greece finally had a gleaming $200 million container for its most treasured antiquities. What mattered was what wasn't there: the sections of the Parthenon frieze known as the Elgin Marbles, which have resided in the British Museum for the last 200 years. At a press conference before the opening, Greek Minister of Culture Antonis Samaras minced no words describing his government's attitude toward England's refusal to repatriate the marbles, high reliefs depicting battle scenes between gods and humans. Now that we have a proper place for them, Samaras said, no Greek can be happy until they are returned. As if the British today should be so consumed with guilt, they couldn't wait to give the things back.

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The marbles have been in England since 1801, when Thomas Bruce, the 7th Lord Elgin, was ambassador to the Ottoman Empire. Concerned for their condition—and possibly obsessed by them—Elgin had them removed at his own expense. It bankrupted him, compelling the marbles' sale to the museum.

To whom do they belong? The question is larger than Greek or British egos. Museums everywhere, especially those that began as ethnographic institutions dedicated to educating their constituents about distant periods and cultures, have objects taken from other parts of the globe. Many were spoils of war. Still, most of us get our first experience of the breadth of history among them.

It's not possible to travel to every country in order to get a sense of it. That's why museums loan precious objects to each other for temporary shows that travel between nations. Early last week a spokesperson for the British Museum held out at least a twig of an olive branch by proposing a 90-day loan of some of the Parthenon sculptures—but only if the Greeks publicly acknowledge that institution as their legal owner.

Fat chance. Characterizing the British as kidnappers who had stolen more than half the 115 original marbles and taken them into "enforced exile," Samaras did not so much plead for their return as express indignation that the British had not offered to right an obvious injustice. He had no problem with the scores of ancient Greek artifacts dispersed among the world's museums. The Elgin Marbles were another story. They represented the soul of the Greek people. Looking at the frieze now, he said, is like seeing a family photograph with half its members missing. "They were made to be seen in sequence," he said. "That can never happen while the marbles are being held hostage in London."

Lost in this ancient debate is the new building itself, a modernist hulk covering an area of 270,000 square feet and offering more than 150,000 square feet of exhibition space. Designed to match the footprint of the Parthenon by Swiss-born New York architect Bernard Tschumi, in association with the Athens-based Michalls Photiadis, it sits in full view of the Acropolis but at some distance below it, in an affluent residential neighborhood that was decimated to make room for it.

The hue and cry raised by those who wanted to preserve the homes that were razed was partly responsible for the years-long delay in construction. The area is among the very few in Athens that did not succumb to wrecking balls in the 1960s, creating what is now an eyesore of a metropolis made of ignominious concrete. The museum project did not really get into gear until the 1980s, when movie star and former Culture Minister Melina Mercouri brought some glamour to a campaign to forge a new national Greek identity, of which the Acropolis Museum is now a transcendent symbol.

“They were made to be seen in sequence,” Samaras said of the Parthenon friezes. “That can never happen while the marbles are being held hostage in London.”

I happened to be at a party on the rooftop terrace of a private home next door to the museum a couple of days before the official opening. Looking down at the site, where a reception for Greek archaeologists, academics, and museum professionals was in progress, it was easy to see how large a swath the construction had cut through the neighborhood, and how out of scale the building was with its surroundings.

During opening week, the museum projected a slide show of its contents on its façade and those of nearby buildings. Animated by a local artist, giant stone horses galloped, soldiers threw spears, and Greek goddesses wore red lipstick on mouths that seemed to open in song. A crowd of passersby watched the show from the street, barred from entering their new national monument by police or security guards who would not permit even a snapshot of the exterior.

There's no question that the museum has priceless objects to protect—4,000 of them, to be exact. But the atmosphere of an institution under siege extended even to those invited to attend its several openings; their numbers were restricted and they were not free to peruse the galleries except when accompanied by staff. It took me more than a week of daily inquiries and many pleas from insiders to get legitimate press approval to attend a preview, which proceeded under the watchful eyes of many guards.

That is not the reason I have mixed feelings about the building. It is not the greatest piece of architecture. From the outside it screams airport terminal and implies something sinister going on inside. But it also reveals more going on underneath. An oblong cut in the pedestrian mall leading to the entrance looks down on ancient streets and homes of no particular distinction that were discovered during construction. Tschumi incorporated the excavation into the building and put a glass floor throughout, so visitors could look down on it as they moved.

The surface can be slippery and the view vertiginous, particularly on the ramp that leads rather ceremoniously up to the second floor. In daylight hours, when the interior lights are off, the view below is a little murky. Lit up at night—the museum is open till 10 p.m.—visibility is better and the excavation, which spectators can visit, looks almost romantic.

In a brief conversation during the preview, Tschumi told me his design was deliberately austere, intended to make the building disappear so the collection of objects had the spotlight. But the second-floor gallery for archaic and classical art is so obscured by thick gray concrete columns that it is literally hard to tell the forest from the trees. Worse, every piece of sculpture is so clean and isolated on its own spotlighted pedestal, with no particular relation to anything around it, that the whole place looks like a giant gift shop in some anonymous ether.

Wending my way between fragile figures of mythical creatures, temple steles or Athena Nikes, my attention was constantly drawn outside the windows, toward the Acropolis, which seemed to hover on its hill—the highest point in Athens—like a wounded angel pleading for mercy. Samaras did have a point.

Installed on the museum's third and topmost floor, in a glass and concrete box angled to mirror the Parthenon ruins, the jaundiced original blocks look pretty bad beside the white plaster copies of the originals in London, making the whole frieze appear to be fake. What's wonderful is being able to see the reliefs, which wrap around the wall of an interior core just above eye level, at such close range. They are an indisputable marvel of craftsmanship. Best is to see the frieze at night, when its reflection in the windows makes it appear whole, except of course for the spaces where blocks were destroyed long ago.

It's just as well that no wax casts exist for copies to be made of those sections. It's not Greece that lacks a soul, but the building made to express it. And though the museum exhibits works long hidden from view, the country doesn't need such a behemoth to muscle itself into contemporary culture. During the week of its opening, Athens played host to the second edition of a fledging biennial of cutting-edge art, actually six exhibitions by independent curators from Greece, Italy, Spain, and the U.S. invited to organize them. On a nearly no-string budget, they managed to bring a vibrant international presence to a burgeoning local art scene.

The point is that whether or not the British return the Elgin Marbles, the Greeks already have it all—the glory of the ancient past and the energy of the constant present. It's too bad they don't seem to know it.

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Linda Yablonsky is the U.S. art critic for Bloomberg News and a Scene & Herd columnist for Artforum.com. Her work has appeared in The New York Times, Art in America, and Art + Auction. She is the author of The Story of Junk: A Novel .