Using a group with Kazhdan’s property (T), in 1991 S. Wassermann constructed a separable C*algebra A whose Ext is not a group. I will show that there is a unital embedding of A into the Calkin algebra such that the relative commutant of its range does not even include a unital copy of a simple, nonabelian C*algebra (a moment of though shows that this implies Ext(A) is not a group).
The motivation for this result comes from the (widely open) question whether the Calkin algebra has a Ktheory reversing automorphism. It implies that the Calkin algebra is not isomorphic to the corona of the stabilization of the Cuntz algebra O_\infty, with which it shares many properties (both algebras are purely infinite and simple, satisfy the double commutant theorem for separable unital subalgebras, have the same Ktheory, and similarly behaved Ext functors).
The proof does not involve logic at all.
