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 K₀(X) in terms of generators and relations in the case G = G^sc/μ₂ is of Dynkin type A or 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.