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We prove the Farrell-Jones Conjecture for (non-connective) Atheory with coefficients and finite wreath products for hyperbolic groups, CAT(0)-groups, cocompact lattices in almost connected Lie groups and fundamental groups of manifolds of dimension less or equal to three. Moreover, we prove inheritance properties such as passing to subgroups, colimits of direct systems of groups, finite direct products and finite free products. These results hold also for Whitehead spectra and spectra of stable pseudo-isotopies in the topological, piecewise linear and smooth category.2010 Mathematics Subject Classification. 19D10, 57Q10, 57Q60.

We prove the A-theoretic Farrell-Jones conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S-arithmetic groups and lattices in almost connected Lie groups.Using this, we can adapt previous work by Rüping [9] and Kammeyer, Lück and Rüping [7] to A-theory:Corollary 1.2. The A-theoretic Farrell-Jones conjecture with coefficients and finite wreath products holds for subgroups of GL n (Q) or GL n (F (t)), where F is a finite field.In particular, the conjecture holds for S-arithmetic groups.Proof. The proof works as the one of [9, Theorem 8.13]: Since the conjecture is inherited under directed colimits [4, Theorem 1.1(ii)], it suffices to consider linear groups over localizations at finitely many primes. Then [9, Proposition 2.2] together with [4, Corollary 6.6]

Abstract. We show that for finite groups the Loday assembly map with coefficients in finite fields is in general not injective.

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