TITLE: Stable cohomology of groups and algebraic varieties.

ABSTRACT: A group cohomology ring has a quotient which has a birational geometric interpretation. It is defined via the quotient spaces of representations of finite groups considered as algebraic varieties. These varieties play the role of universal spaces with respect to rational maps in this theory.

This construction allows defining nonramified elements in the ring of stable cohomology. These are birational invariants of the quotient varieties. The quotient spaces play the role of universal spaces for nonramified elements too.

In spite of its algebro geometric nature this cohomology invariants in many cases can be described in pure group theoretic terms.