Factorization homology is a method for constructing quantum field theories from \(\mathbb{E}_n\)-algebras. We describe a genuine \(G\)-equivariant version of factorization homology for a finite group \(G\). A \(G\)-factorization homology theory assigns to each smooth manifold with an action of a subgroup \(H < G\) a genuine \(H\)-spectrum. Following Ayala and Francis we give an axiomatic characterization of such theories as satisfying a monoidal version of excision and intertwining topological induction of manifolds with multiplicative transfer of spectra. As a future application we present real THH as genuine \(\mathbb{Z}/2\)-factorization homology.