Submission: 2012, Nov 14
For the Grothendieck group of a split simple linear algebraic group, the twisted gamma-filtration provides a useful tool for constructing torsion elements in gamma-rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element in the gamma-ring of a complete flag variety twisted by means of a PGO-torsor. This generalizes the construction in the HSpin case previously obtained by Zainoulline. We use this torsion element to study algebras with orthogonal involutions.
2010 Mathematics Subject Classification: 20G15; 14C25; 14L30; 16W10
Keywords and Phrases: linear algebraic group, Tits algebra, gamma filtration, Grothendieck group K_0, torsion, algebras with orthogonal involution
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