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.