Transitivity of one-step dynamical Cuntz subequivalence

Determine whether one-step dynamical Cuntz subequivalence is transitive for arbitrary actions of discrete groups on C*-algebras.

Background

The paper distinguishes one-step (or strongly) dynamically Cuntz subequivalence from its transitive closure. Dynamical Cuntz subequivalence is obtained by allowing finite chains of intermediate comparisons, but it is not established that a single one-step comparison relation is already transitive in general.

The authors note that transitivity is known under the additional hypotheses of real rank zero and stable rank one, leaving the general case unresolved.