Assembly maps with coefficients in topological algebras and the integral K-theoretic Novikov conjecture

We prove that any countable discrete and torsion free subgroup of a general linear group over an arbitrary field or a similar subgroup of an almost connected Lie group satisfies the integral algebraic -theoretic (split) Novikov conjecture over and where denotes the -algebra of compact operators and denotes the algebra of Schatten class operators. We introduce assembly maps with finite coefficients and under an additional hypothesis, we prove that such a group also satisfies the algebraic -theoretic Novikov conjecture over and with finite coefficients. For all torsion free Gromov hyperbolic groups we demonstrate that the canonical algebra homomorphism induces an isomorphism between their algebraic -theory groups.