  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 ${\rm A}$ or ${\rm C}$
(here $G^{sc}$ 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.

Algebraic Geometry