  Paschke duality identifies the K-homology of a space X with the K-theory of a
certain dual C*-algebra. We show that Paschke's dual algebra is in a natural
way the algebra of sections of a certain sheaf of C*-algebras over X, which can
be thought of as a sheaf of noncommutative symbols. This conceptually
simplifies a number of constructions in K-homology, such as the association of
a homology class to an elliptic operator and the construction of assembly maps.
