A Farrell-Jones Isomorphism for K-theory of PolyhedraWe prove that the cut-and-paste K-theory of polyhedra, also called scissors
congruence K-theory, is a homotopy orbit spectrum. More generally, we show that
a broad class of algebraic K-theory constructions, based on covering families,
all commute with the formation of homotopy orbits. In other words, "K-theory of
coverings" always has a Farrell-Jones type isomorphism. Finally, we introduce a
trace map for K-theory of coverings, and use it to prove the existence of some
classes in the higher K-theory of polyhedra.
arxiv.org