An etale approach to the Novikov conjecture
  We show that the rational Novikov conjecture for a group   $\Gamma$ of finite homological type follows from the mod 2   acyclicity of the Higson compactifcation of an E$\Gamma$. We then   show that for groups of finite asymptotic dimension the Higson   compactification is mod p acyclic for all p, and deduce the integral   Novikov conjecture for these groups. 
A. Dranishnikov, S. Ferry and S. Weinberger