In this talk I would like to present ongoing joint work with J. Christensen and R. Neagu. Our main goal is to construct a wealth of completely new examples of flows (i.e. actions of the reals R) on classifiable stably projectionless C*-algebras. It has been relatively unexplored how rich the class of flows on such algebras truly is. The only published result about this topic is an article by Kishimoto-Kumjian, who show that for certain UHF-stable, stable, projectionless C*-algebras with a unique unbounded trace (up to multiples), there exists a trace-scaling flow. However, it is a priori completely open if one can find flows on C*-algebras with more traces that scale different extremal traces at different speeds. Another open issue, which has only been studied in the unital case in a sole article of Kishimoto, is what possible pairings between invariant traces and the K_1-group can arise as Connes' rotation map associated to a flow on the C*-algebra. The main result of our work in progress is that any combination of these two abstract invariants is realized when the underlying C*-algebra A is classifiable, stable, and has trivial pairing map between traces and K_0. I shall make both the involved concepts and the statement of our result more rigorous during the talk.
