THE K-THEORY OF VERSAL FLAGS AND COHOMOLOGICAL INVARIANTS OF DEGREE 3

Abstract

Let G be a split semisimple linear algebraic group over a field and let X be a generic twisted flag variety of G. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the Grothendieck ring K-0(X) in terms of generators and relations in the case G = G(sc) / mu(2) is of Dynkin type A or C (here Gsc is the simply-connected cover of G); we compute various groups of (indecomposable, semi-decomposable) cohomological invariants of degree 3, hence, generalizing and extending previous results in this direction.