A simple AF algebra not isomorphic to its opposite
  We show that it is consistent with ZFC that there is a simple nuclear non-separable 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 O_2, or of the CAR algebra. 
Ilijas Farah and Ilan Hirshberg
math.OA math.LO