A Controlled Approach to the Isomorphism Conjecture
  We use a hocolim approach to the Isomorphism Conjecture in K-Theory to analyze the case of groups of the form $G\rtimes Z$ and $G_1*_{G}G_2$. As an important corollary we prove that the isomorphism conjecture in K-Theory holds for a finitely generated free group. 
Daniel Juan-Pineda and Stratos Prassidis