Calkin algebra, Kazhdan's property (T), strongly self-absorbing C*-algebras

The Calkin algebra is not isomorphic to the corona of the stabilization of the Cuntz algebra~${\mathcal{O}}_{\mathrm{\infty }}$, any other Kirchberg algebra, or even the corona of the stabilization of any unital, $\mathcal{Z}$-stable ${\mathrm{C}}^{\ast }$-algebra. The proof relies on properties of relative commutants of separable ${\mathrm{C}}^{\ast }$-subalgebras.