On the K-theory of groups with finite asymptotic dimension

It is proved that the assembly maps in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups F with finite asymptotic dimension that admit a finite model for (E) under bar Gamma. The result also applies to certain groups that admit only a finite dimensional model for (E) under bar Gamma. In particular, it applies to discrete subgroups of virtually connected Lie groups.