Simple nuclear C*-algebras not isomorphic to their opposites [Mathematics]

We show that it is consistent with Zermelo–Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C∗C∗-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2O2 or of the canonical anticommutation relations (CAR) algebra.