Principal groupoid C*-algebras with bounded trace
  Suppose G is a second countable, locally compact, Hausdorff, principal groupoid with a fixed left Haar system. We define a notion of integrability for groupoids, and show G is integrable if and only if the groupoid C*-algebra C*(G) has bounded trace. 
Lisa Orloff Clark (Susquehanna University), Astrid an Huef (University   of New South Wales)