A twisted flag variety is a variety that becomes isomorphic to a flag variety over a separable closure of the base field F, such as Severi–Brauer varieties and smooth projective quadrics. Panin (1994) showed that the Quillen K-theory of such a variety is isomorphic to the K-theory of a semisimple F-algebra canonically associated with it, a product of central simple algebras first introduced by Tits. I will introduce twisted flag varieties and explain this result for inner forms, using Severi–Brauer varieties as the main example.