We construct a simple, nuclear, stably projectionless C*-algebra W which hastrivial K-theory and a unique tracial state, and we investigate the extent towhich W might fit into the hierarchy of strongly self-absorbing C*-algebras asan analogue of the Cuntz algebra O_2. In this context, we show that everynondegenerate endomorphism of W is approximately inner and we construct atrace-preserving embedding of W into the central sequences algebra M(W)_\infty\cap W'. We conjecture that W\otimes W is isomorphic to W and we note someimplications of this, for example that W would be absorbed tensorially by acertain class of nuclear, stably projectionless C*-algebras. Finally, weexplain why W may play some role in the classification of such algebras.
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