A simple separable exact C*-algebra not anti-isomorphic to itself

We give an example of an exact, stably finite, simple, separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^∞ UHF algebra. We can also explicitly compute the K-theory of D, namely ${K_0 (D) \cong {\mathbb{Z}} \tfrac{1}{3}]}$ with the standard order, and K ₁ (D) =  0, as well as the Cuntz semigroup of D, namely ${W (D) \cong {\mathbb{Z}} \tfrac{1}{3} ]_{+} \sqcup (0, \infty).}$