In ordinary algebraic topology the Adams spectral sequence can be applied for any cohomology theory $E$ and in good cases it converges to the stable homotopy classes of maps (of the E-nilpotent completion) of some chosen spaces $X,Y$. I guess that similar results are know for equivariant cohomology theories. I am looking for something like a generalization of Greenlees "Stable Maps into Free $G$-Spaces".

Q.: Is it true that such more general statements exist? Where can I find them?