Let $\mathcal{A}$ be a C$^*$ -algebra. Let $\mathcal{A}^{op}$ denote the opposite algebra, that is, the C$^*$ -algebra given as a set the same as $\mathcal{A}$, where addition is the same as before, but multiplication is switched. I have heard that it is an open question whether every stably finite classifiable C$^*$ -algebra is isomorphic to it's opposite algebra.
My question is, a-priori, what is known about the connection between $Ell(\mathcal{A})$ and $Ell(\mathcal{A}^{op})$ for $\mathcal{A}$ stably finite?