A genuine G‐spectrum for the cut‐and‐paste K‐theory of G‐manifolds

Abstract Recent work has applied scissors congruence ‐theory to study classical cut‐and‐paste () invariants of manifolds. This paper proves the conjecture that the squares ‐theory of equivariant ‐manifolds arises as the fixed points of a genuine ‐spectrum. Our method utilizes the framework of spectral Mackey functors as models for genuine ‐spectra, and our main technical result is a general procedure for constructing spectral Mackey functors using squares ‐theory.