Equivariant invariants for algebraic varieties with finite action

Abstract: 

We describe a road map from  equivariant motivic homotopy to equivariant motivic homology and several properties of these categories. We also describe the connections of Bredon motivic cohomology with equivariant higher Chow groups introduced initially by Totaro and generalized by Edidin and Graham. This is a joint work with J.Heller (University of Illinois, Urbana-Champaign) and P.A.Ostvaer (University of Oslo).