We generalize Wagoner's representation of the automorphism group of a two-sided subshifts of finite type as the fundamental group of a certain CW-complex to groupoids having a certain refinement structure. This significantly streamlines the original proof and allows us to extend this construction to, e.g., the automorphism group of subshifts of finite type over arbitrary finitely generated groups and the automorphism group of G-SFTs.
