On the $K$–theory of subgroups of virtually connected Lie groups

Abstract

We prove that for every finitely generated subgroup $G$ of a virtually connected Lie group which admits a finite-dimensional model for $\underset{¯}{E}G$, the assembly map in algebraic $K$–theory is split injective. We also prove a similar statement for algebraic $L$–theory which, in particular, implies the generalized integral Novikov conjecture for such groups.