Algebraic Cycles and Equivariant Cohomology Theories

Abstract

this paper is that algebraic cycles provide interesting non-trivial invariants for finite groups, as well as new equivariant cohomology theories which answer natural questions in equivariant homotopy theory. Besides being quite computable, these theories carry Chern classes for representations and have deep relations with usual Borel cohomology theory. In fact their coe#cients are simpler than standard group cohomology and have a geometric interpretation of independent interest. Among their main properties, we shall prove a full equivariant analogue of the Segal loop space conjecture proved in [3]