On the algebraic K-theory of some homogeneous varieties
Doc. Math., J. DMV 17, 167-193 (2012)
Summary: The $K$-theory of inner twisted forms of homogeneous varieties $G/H$ with connected reductive algebraic groups $H\subset G$ of the same rank is computed. We provide an explicit isomorphism with the $K$-theory of certain central simple algebras associated to the considered variety, as a consequence one has that $K_0(G/H)$ is a free abelian group of rank $[W(G):W(H)]$. The result is used for the computation of the $K$-theory of some affine homogeneous varieties including an octonionic projective plane and quaternionic projective spaces.
Mathematics Subject Classification
affine homogeneous varieties, K-theory, central simple algebras