Geodesic
On the algebraic K-theory of some homogeneous varieties
Documenta mathematica, Tome 17 (2012), pp. 167-193.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 19E08, 14M17
Keywords: affine homogeneous varieties, K-theory, central simple algebras 
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     author = {Ananyevskiy, Alexey},
     title = {On the algebraic {K-theory} of some homogeneous varieties},
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Ananyevskiy, Alexey. On the algebraic K-theory of some homogeneous varieties. Documenta mathematica, Tome 17 (2012), pp. 167-193. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a23/