On a simple unital projectionless C*-algebra

We construct a unital separable C*-algebra Z as an analog of the hyperfinite type II₁ factor. Besides being nuclear, simple, projectionless, and infinite-dimensional, Z has a unique tracial state, and is KK-equivalent to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], the algebra of complex numbers. It is shown that unital endomorphisms on Z are approximately inner, and that Z is isomorphic to the infinite tensor product of its replicas. It is also shown that A ≅ Z ⊗ A for certain interesting classes of unital simple nuclear C*-algebras A of real rank zero.