On the algebraic K-theory of some homogeneous varieties

Abstract

The K-theory of inner twisted forms of homogeneous varieties G/ with connected reductive algebraic groups H ⊂ 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 K0(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.