Rigidity theorems for K- and H-cohomology and other functors

Suslin proved that for an extension K/k of algebraically closed fields the induced maps K_m(k)[n] --> K_m(K)[n] and K_m(k)/n —> K_m(K)/n for the higher K-groups are isomorphisms, where A[n] is the subgroup of n-torsion in an abelien group, and A/n = A/nA, by definition. In this paper we generalize this to other functors and other field extensions.