Compact operators and algebraic K-theory for groups which act properly and isometrically on Hilbert space.

GUILLERMO CORTIÑAS; GISELA TARTAGLIA

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK

WALTER DE GRUYTER & CO

Lugar: Berlin; Año: 2018 vol. 734 p. 265 - 292

0075-4102

We prove the K-theoretic Farrell?Jones conjecture for groups with theHaagerup approximation property and coefficient rings and C-algebras which are stable withrespect to compact operators. We use this and Higson?Kasparov?s result that the Baum?Connesconjecture holds for such a group G, to show that the algebraic and the C-crossed product ofG with a stable separable G-C-algebra have the same K-theory.