Equivariant factorization homology of global quotient orbifolds

Abstract

We introduce equivariant factorization homology, extending the axiomatic framework of Ayala-Francis to encompass multiplicative invariants of manifolds equipped with finite group actions. Examples of such equivariant factorization homology theories include Bredon equivariant homology and (twisted versions of) Hochschild homology. Our main result is that equivariant factorization homology satisfies an equivariant version of tensor excision, and is uniquely characterised by this property. We also discuss applications to representation theory, such as constructions of categorical braid group actions.