A simple, monotracial, stably projectionless C*-algebra

We construct a simple, nuclear, stably projectionless C∗-algebra W which has trivial Ktheory and a unique tracial state, and we investigate the extent to which W might fit into the hierarchy of strongly self-absorbing C∗-algebras as an analogue of the Cuntz algebra O2. In this context, we show that every nondegenerate endomorphism of W is approximately inner and we construct a tracepreserving embedding of W into the central sequences algebra M(W )∞ ∩W ′. We conjecture that W⊗W ∼= W and we note some implications of this, for example that W would be absorbed tensorially by a certain class of nuclear, stably projectionless C∗-algebras. Finally, we explain why W may play some role in the classification of such algebras.