Abstract: In this talk, I consider a G-equivariant Borel Floer theory for 3-manifolds equipped with a G-action and consider what such a theory implies about the non-equivariant Floer theories of the manifold Y and its quotient. In particular, by defining a G-equivariant contact class, I shall demonstrate a relationship between the contact topology of a mod p L-space Y and of any manifold p-fold covered by Y.