Equivariant metric for smooth moduli spaces

Let M be a smooth oriented closed 4-manifold. Suppose that a finite group G acts smoothly on M. Let P : E → M be an SU(2)-vector bundle over M with a smooth G-action such that P is a G-map. In this paper we would like to study the existence of a G-invariant metric for the smooth G-moduli space of anti-self-dual connections of E except the reducible singularities when the instanton number of k of E is large enough.