The C2-equivariant cohomology of complex projective spaces

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations C2, using ordinary graded on fundamental groupoid, with coefficients in Burnside ring Mackey functor. This extension RO(C2)-graded theory allows for definition Euler classes, which are used as generators spaces. As an application, we give version Bézout's theorem.