Localization algebras and duality

The paper studies the dual algebras of localization Roe algebras over proper metric spaces and develops a localization version of Paschke duality for K-homology. It is shown that the localization K-homology groups are isomorphic to Kasparov's K-homology groups for the Rips complex of proper metric spaces with bounded geometry. It follows that the obstruction groups to the coarse Baum-Connes conjecture can also be derived from the dual localization algebras.