  It is proved that the assembly map in algebraic K- and L-theory with respect
to the family of finite subgroups is injective for groups $\Gamma$ with finite
quotient finite decomposition complexity (a strengthening of finite
decomposition complexity introduced by Guentner, Tesser and Yu) that admit a
finite dimensional model for $\underbar E\Gamma$ and have an upper bound on the
order of their finite subgroups. In particular this applies to finitely
generated linear groups over fields with characteristic zero with a finite
dimensional model for $\underbar E\Gamma$.
