  We present a version of higher Hochschild homology for spaces equipped with
principal bundles for a structure group $G$. As coefficients, we allow
$E_\infty$-algebras with $G$-action. For this homology theory, we establish an
equivariant version of excision and prove that it extends to an equivariant
topological field theory with values in the $(\infty,1)$-category of cospans of
$E_\infty$-algebras.
