A generalization of the Jiang-Su construction

Let G be a countable abelian group. We construct a unital simple projectionless C∗-algebra A with a unique tracial state, that satisfies (K0(A), [1A]) ∼= (Z, 1), K1(A) ∼= G, A ⊗ Z ∼= A, and that is obtained as the inductive limit C∗-algebra of a sequence of dimension drop algebras of a specific form. This construction is based on the construction of the Jiang-Su algebra. By this construction, we show a certain conjugacy result for aperiodic automorphisms of these projectionless C∗-algebras. We also show that an automorphism of this projectoinless C∗-algebra has a certain aperiodicity up to the weakly inner automorphisms in the tracial representation if and only if it has a kind of Rohlin property, which leads to the Rohlin property after taking tensor product of certain C∗-algebras of real rank zero. 2000 Mathematics Subject Classification. Primary 46L35; Secondary 46L80, 46L40.