Title: Approaching the UCT problem via crossed products of the Razak-Jacelon algebra,
Abstract: We show that the UCT problem for separable, nuclear $\mathrm C^*$-algebras
relies only on whether the UCT holds for crossed products of certain finite
cyclic group actions on the Razak-Jacelon algebra. This observation is
analogous to and in fact recovers a characterization of the UCT problem in
terms of finite group actions on the Cuntz algebra $\mathcal O_2$ established
in previous work by the authors. Although based on a similar approach, the new
conceptual ingredients in the finite context are the recent advances in the
classification of stably projectionless $\mathrm C^*$-algebras, as well as a
known characterization of the UCT problem in terms of certain tracially AF
$\mathrm C^*$-algebras due to Dadarlat.