Extensions of C(X) by simple C*-algebras of real rank zero

Let Ext(C(X),A) be the set of unitarily equivalence classes of essential C*-algebra extensions of the following form: 0 --> A --> E --> C(X) --> 0, where A is a nonunital separable simple C*-algebra of real rank zero, stable rank one with unique normalized trace and X is a finite CW complex. We show that there is a bijection J: Ext(C(X),A) --> KK(C(X),M(A)/A), where M(A) is the multiplier algebra of A. In particular, we determine when an extension is actually splitting. We also, in a more general setting, give a condition when an essential extension is quasidiagonal.