Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic K-theory. In this talk I present a new application of their framework to the study of cut-and-paste invariants of manifolds. We construct a spectrum that recovers the classical SK (“schneiden und kleben,” German for “cut and paste”) groups for manifolds on the zeroth homotopy group, and we construct a lift of the Euler characteristic, one of these invariants, to a map of spectra. This is joint work with M. Merling, L. Murray, C. Rovi and J. Semikina.