The range of a class of classifiable separable simple amenable C∗C∗-algebras

We study the range of a classifiable class AA of unital separable simple amenable C∗C∗-algebras which satisfy the Universal Coefficient Theorem. The class AA contains all unital simple AH-algebras. We show that all unital simple inductive limits of dimension drop circle C∗C∗-algebras are also in the class. This unifies some of the previous known classification results for unital simple amenable C∗C∗-algebras. We also show that there are many other C∗C∗-algebras in the class. We prove that, for any partially ordered simple weakly unperforated rationally Riesz group G0G0 with order unit u  , any countable abelian group G1G1, any metrizable Choquet simplex S  , and any surjective affine continuous map r:S→Su(G0)r:S→Su(G0) (where Su(G0)Su(G0) is the state space of G0G0) which preserves extremal points, there exists one and only one (up to isomorphism) unital separable simple amenable C∗C∗-algebra A   in the classifiable class AA such that((K0(A),K0(A)+,[1A]),K1(A),T(A),λA)=((G0,(G0)+,u),G1,S,r).((K0(A),K0(A)+,[1A]),K1(A),T(A),λA)=((G0,(G0)+,u),G1,S,r).