  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.
