Abstract: In foundational work, McDuff and Segal proved “homological stability” in the setting of unordered configuration spaces $C_n(M)$ of $n$ points in an open manifold $M$; that is, $H_d(C_n(M)) \cong H_d(C_{n+1}(M))$ for $n\gg d$. In joint work with J.D. Quigley and Chase Vogeli, we prove an equivariant generalization of McDuff and Segal’s result which applies to Bredon homology of unordered configuration spaces on G-manifolds for a finite abelian group G.