The Pontryagin-Thom theorem for families of framed equivariant manifolds

The Pontryagin-Thom theorem gives an isomorphism from the cobordism group of framed $n$-manifolds to the $n$th stable homotopy group of the sphere spectrum. In this paper, we prove the generalization of the Pontryagin-Thom theorem for families of framed equivariant manifolds parameterized over a compact base space.