Suppose that G is a group acting on a fibre bundle (F,E,B) by bundle automorphisms. In this case, the action automorphisms E-->E give the integral homology H_{}(E;Z) the structure of a G-module. Also, the action automorphisms F-->F and B-->B give each module H_p(B;H_q(F;Z)) the structure of a G-module. Can the Serre spectral sequence of the fibre bundle be made G-equivariant in the sense of being a spectral sequence of G-modules converging to H_{}(E;Z), and with second page E_{p,q}=H_p(B;H_q(F)) (considered as G-modules in the above sense)?

Thanks!