The integral K-theoretic Novikov conjecture for groups with finite asymptotic dimension

The integral assembly map in algebraic K-theory is split injective for any geometrically finite discrete group with finite asymptotic dimension. The goal of this paper is to apply the techniques developed by the first author in to verify the integral Novikov conjecture for groups with finite asymptotic dimension as defined by M. Gromov. Recall that a finitely generated group Γ can be viewed as a metric space with the word metric associated to a given presentation.