Classification of certain simple C*-algebras with torsion in K-1

We show that the Elliott invariant is a classifying invariant for the class of C*-algebras that are simple unital infinite dimensional inductive limit s of finite direct sums of building blocks of the form {f is an element of C(T) circle times M-n : f(x(i)) is an element of M-d i, i = 1,2,...,N}, where x(1), x(2),...x(N) is an element of T, d(1), d(2),...,d(N) are intege rs dividing n, and M-d i is embedded unitally into M-n. Furthermore we prov e existence and uniqueness theorems for *-homomorphisms between such algebr as and we identify the range of the invariant.