Using a residually finite 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 an extension of A (in the Calkin algebra) such that the relative commutant of its range does not even include a unital copy of a simple, nonabelian C*-algebra (this easily implies that Ext(A) is not a group). The original motivation for this result comes from the (widely open) question whether the Calkin algebra has a K-theory reversing automorphism. I?ll say a word on this, but more importantly, there is a possibility that this construction may give new examples of C*-algebras without the UCT (alas, all of them non-nuclear).