Scissors congruence KK‐theory for equivariant manifolds

We introduce a scissors congruence ‐theory spectrum that lifts the equivariant scissors congruence groups for compact ‐manifolds with boundary, and we show that on , this is the source of a spectrum‐level lift of the Burnside ring‐valued equivariant Euler characteristic of a compact ‐manifold. We also show that the equivariant scissors congruence groups for varying subgroups assemble into a Mackey functor, which is a shadow of a conjectural higher genuine equivariant structure.