Abstract: For an algebraic group G over an arbitrary field F, the geometry of projective homogeneous G-varieties has yet to be fully classified. A effective tool used towards such a classification is the cohomological invariant given by the set of Tits algebras of G. A result of Panin provides a connection from the Tits algebras of G to the Grothendieck group of G, and in particular to its associated gamma-filtration. In this talk, we use the Tits algebras of G to construct a torsion element in the gamma-filtration of a flag variety twisted by means of a PGO-torsor. This generalizes a construction in the HSpin case previously obtained by Zainoulline.