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For the Grothendieck group of a split simple linear algebraic group, thetwisted gamma-filtration provides a useful tool for constructing torsionelements in gamma-rings of twisted flag varieties. In this paper, we constructa non-trivial torsion element in the gamma-ring of a complete flag varietytwisted by means of a PGO-torsor. This generalizes the construction in theHSpin case previously obtained by Zainoulline. We use this torsion element tostudy algebras with orthogonal involutions.

Twisted gamma filtration and algebras with orthogonal involution