Cohomology Ring of Orbits

In this paper, we investigate the integer graded and RO(G)-graded equivariant cohomologies. Combined with the homotopical equivariant singular cohomology we obtain the equivariant cohomology ring of an orbit with the Gal(C/R) action, which is a fundamental model of equivariant spaces with group action. We may in the future to generalize the result to the general equivariant cohomology of an arbitrary equivariant space.