Title: KMS states on the C*-algebras of Fell bundles over groupoids,
Abstract: We consider fiberwise singly generated Fell-bundles over etale groupoids.
Given a continuous real-valued 1-cocycle on the groupoid, there is a natural
dynamics on the cross-sectional algebra of the Fell bundle. We study the
Kubo-Martin-Schwinger equilibrium states for this dynamics. Following work of
Neshveyev on equilibrium states on groupoid C*-algebras, we describe the
equilibrium states of the cross-sectional algebra in terms of measurable fields
of traces on the C*-algebras of the restrictions of the Fell bundle to the
isotropy subgroups of the groupoid. As a special case, we obtain a description
of the trace space of the cross-sectional algebra. We apply our result to
generalise Neshveyev's main theorem to twisted groupoid C*-algebras, and then
apply this to twisted C*-algebras of strongly connected finite k-graphs.