The oligarch is hungry. So Dmitry Firtash crams into a small elevator with his entourage. Slowly, they rise to the private rooftop level of Do & Co, a modernist hotel in the otherwise Old World tourist heart of Vienna. The doors open into a tiny, glass-walled private dining room that seems like a long catwalk suspended in air, affording the oligarch a 360-degree view of the European capital he’s called home the past three years. Downstairs, he’s left behind his two bodyguards, who will spend the evening glowering at anyone entering or leaving the elevator. Up here, he’s exposed yet insulated—a billionaire in a gilded cage.