Remarks on the extension group for purely infinite corona algebras

We study BDF theory in the context of (not necessarily simple) purely infinite corona algebras. Let B be a nonunital separable simple C*-algebra with standard regularity properties for which C(B) is purely infinite (though not necessarily simple). Let A be a separable nuclear C*-algebra. We prove a BDF Voiculescu decomposition theorem for maps from A to C(B), and use this to prove that Ext(sigma) (A, B) is a group. Then, restricting to the caseA = C(X), for some compact metric space X, and B has continuous scale, we provide characterizations of the neutral element for Ext(C(X), B).