Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, $f:X\to Y$ be a map between closed manifolds and $a\in Y$. The vanishing of the Nielsen root number $N(f;a)$ implies that f is homotopic to a root free map h, i.e., $h～f$ and $h^{?1}(a)=?$. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group.