The Kirchberg-Rordam character question: does absence of characters on the central sequence algebra characterize Jiang-Su stability?

Theorem 1.1: for every nonzero unital separable complex C*-algebra $A$ and every free ultrafilter $\omega$, $F_\omega(A)$ has no characters iff $A\cong A\otimes_{\min}\mathcal Z$; no nuclearity, simplicity, trace or comparison hypothesis. Theorem 1.2: every nonzero unital characterless $D$ admits a unital map $I(2,3)\to D^{\otimes_{\max}m}$ for some $m$. Corollary: the infinite minimal tensor power of a nonzero unital separable characterless algebra is $\mathcal Z$-stable (bearing on Kirchberg-Rordam Question 3.7, via Dadarlat-Toms). Not shown: any finite tensor power is $\mathcal Z$-stable, or nonseparable cases.

Theorem 1.1: for every nonzero unital separable complex C*-algebra $A$ and every free ultrafilter $\omega$, $F_\omega(A)$ has no characters iff $A\cong A\otimes_{\min}\mathcal Z$; no nuclearity, simplicity, trace or comparison hypothesis. Theorem 1.2: every nonzero unital characterless $D$ admits a unital map $I(2,3)\to D^{\otimes_{\max}m}$ for some $m$. Corollary: the infinite minimal tensor power of a nonzero unital separable characterless algebra is $\mathcal Z$-stable (bearing on Kirchberg-Rordam Question 3.7, via Dadarlat-Toms). Not shown: any finite tensor power is $\mathcal Z$-stable, or nonseparable cases.