on the $G$-space $B$ defined as the functor $$\pi _n ({\mathcal F}): \operatorname{Or}_{G}\to {\mathcal L}$$ which sends $G/H$ to $(B^H, \pi _n ({\mathcal F}^H))$ and $\hat{a}$ to $(a,a_*)$ where $\pi _n ({\mathcal F}^H):\Pi(B^H)\to {\mathcal Ab}$ is the functor which sends $b \in B$ to $\pi _n (p^{-1}(b)^H)$ and sends a path $\gamma $ with $\gamma(0)=c$ and $\gamma(1)=b$ to a homomorphism from $\pi _n (p^{-1}(b)^H)$ to $\pi _n (p^{-1}(c)^H)$ which is induced by a map admissible over $\gamma $ (see [@whitehead page 185]).

Let $(X,A)$ be a finite $G$-CW-complex, $p:E\to B$ be a $G$-fibration, and $u:X\to E$ be a $G$-equivariant map. As above, assume that for all $H\leq G$ and for all $b\in B$, the space $p^{-1}(b)^H$ is a path connected simple space, and let $\pi _q ({\mathcal F})$ be the $G$-equivariant local coefficient system on $B$ which was introduced above. By abuse of notation, we will again write $\pi _q ({\mathcal F})$ for the $G$-equivariant local coefficients system on $X$ induced from $\pi _q ({\mathcal F})$ via the map $p\circ u$. Let $F_u(X,A;E,B)^G$ denote the space of all equivariant maps $v:X\to E$ such that $v|_A=u|_A$ and $p\circ v=p\circ u$ with compact open topology.

\[thm:equivFedererSS\] There is a spectral sequence with 