On the<i>K</i>-theory of groups with finite decomposition complexity

Abstract

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 Γ with finite quotient finite decomposition complexity (a strengthening of finite decomposition complexity introduced by Guentner, Tessera and Yu) that admit a finite-dimensional model for E ̲ Γ 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 E ̲ Γ .