In this talk, we give the equivariant generalizations of the EHP sequence for G = C2. And then, we calculate RO(C2)-graded cohomology of some C2-equivariant Eilenberg-Mac Lane spaces as a module over the cohomology of a point. Lastly, we give the C2-Lambda algebra, which are the systematic tools for computations of the homotopy groups of spheres in classical case.