  Given a selfmap $f:X\to X$ on a compact connected polyhedron $X$, H. Schirmer
gave necessary and sufficient conditions for a nonempty closed subset $A$ to be
the fixed point set of a map in the homotopy class of $f$. R. Brown and C.
Soderlund extended Schirmer's result to the category of fiber bundles and
fiber-preserving maps. The objective of this paper is to prove an equivariant
analogue of Brown-Soderlund theorem result in the category of $G$-spaces and
$G$-maps where $G$ is a finite group.
