The Kirchberg–Rørdam character criterion

We prove the Kirchberg–Rørdam character criterion: for every free ultrafilter on ℕ, a nonzero unital separable complex C${}^{\ast }$-algebra absorbs the Jiang–Su algebra if and only if its norm central-sequence algebra has no characters. We also prove that the infinite minimal tensor power of every nonzero unital separable complex C${}^{\ast }$-algebra without characters is $\mathcal{Z}$-stable and contains a unital copy of $\mathcal{Z}$.