Embedding an AH-Algebra into a Simple C*-Algebra with Prescribed KK-Data

Let X be a connected finite CW complex. We show that, given a positive homomorphism Hom(K_*(C(X)), K_*(A)) with [1_C(X)][1_A], where A is a unital separable simple C^*-algebra with real rank zero, stable rank one and weakly unperforated K₀(A), there exists a homomorphism h: C(X)A such that h induces . We also prove a structure result for unital separable simple C^*-algebras A with real rank zero, stable rank one and weakly unperforated K₀(A), namely, there exists a simple AH-algebra of real rank zero contained in A which determines the K-theory of A.