Equivariant higher Hochschild homology and topological field theories

We present a version of higher Hochschild homology for spaces equipped with principal G-bundles. As coefficients we allow $E_\infty$-algebras with G-action. For this homology theory we establish an  equivariant version of excision to prove that it extends to an equivariant topological field theory with values in the $(\infty,1)$-category of co-spans in $E_\infty$-algebras. As an example we construct equivariant Dijkgraaf-Witten theories.  This is joint work in progress with Lukas Woike.