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Discussions of Oscar and ethnicity go way back but they usually focus, rather simplistically, on the black & white topic. Since Umeki's Oscar win I believe only four actresses of Asian descent have made the Oscar shortlist: Shohreh Aghdashloo (03), The Tilly sisters (a decade apart in 85 and 94), and Rinko Kikuchi just last year. And they're all in the supporting category [src]
There've been more men. But unless I'm forgetting someone and apart from arguably Ken Watanabe (The Last Samurai) no major Asian movie stars have ever been nominated for an Oscar. Most of the nominees have not been particularly famous prior to their honors. In other words there's no Tony Leungs, Gong Lis, Toshirô Mifunes, Aishwarya Rais or Maggie Cheungs in Oscar's history book.