Twisted constructions in group cohomology and applications
to representation theory
Abstract: We introduce a variation of Evens wreath construction in group cohomology. This construction is applied to answer various classical questions in group cohomology, representation theory and homotopy theory. For example:
1. We compute explicit formulas for the characteristic classes of certain wreath representations, generalizing results of L. Evens. As a corollary we provide algebraic formulas for the characteristic classes of induced bundles and induced representations. This provides a very conceptual answer to an old question posed by M. Atiyah.
2. We prove the conjectured functoriality of Fulton-MacPherson's multiplicative transfer in ordinary cohomology and show that this transfer comes from a generalized cohomology theory.
We finally show how these constructions arise in an algebraic geometric setting and indicate their relation to the motivic homotopy theory developed by V. Voevodsky.