Classification of homomorphisms into simple Z-stable C ∗-algebras

We classify unital monomorphisms into certain simple Z-stable C ∗-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C ∗-algebra, or any unital simple separable nuclear Z-stable C ∗-algebra satisfying the UCT such that C ⊗ B is of tracial rank zero for a UHF algebra B. The target algebra A is allowed to be any unital simple separable Z-stable C ∗- algebra such that A ⊗ B has tracial rank zero for a UHF algebra B, or any unital simple separable exact Z-stable C ∗-algebra whose projections separate traces and whose extremal traces are finitely many. © 2010 Elsevier Inc. All rights reserved