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We study the characteristic map of algebraic oriented cohomology of completespin-flags and the ideal of invariants of formal group algebra. As anapplication, we provide an annihilator of the torsion part of the$\gamma$-filtration. Moreover, if the formal group law determined by theoriented cohomology is congruent to the additive formal group law modulo 2,then at degree 2 and 3, the $\gamma$-filtration of complete spin-flags istorsion free.

On the \gamma-filtration of oriented cohomology of complete spin-flags