Trace class operators, regulators, and assembly maps in K-theory

Abstract

Let G be a group and let KH be homotopy algebraic K-theory. We prove that if G satisfies the rational KH isomorphism conjecture for the group algebra L 1 [G] with coefficients in the algebra of trace-class operators in Hilbert space, then it also satisfies the Ktheoretic Novikov conjecture for the group algebra over the integers, and the rational injectivity part of the Farrell-Jones conjecture with coefficients in any number field.