Non-traditional Cartan subalgebras in twisted groupoid C*-algebras

Well-known work of Renault shows that if ℰ is a twist over a second countable, effective, étale groupoid G, then there is a naturally associated Cartan subalgebra of the reduced twisted groupoid C*-algebra C^*_r(G;ℰ), and that every Cartan subalgebra of a separable C*-algebra arises in this way. However twists over non-effective groupoids can also possess Cartan subalgebras. For twists over étale groupoids built from continuous 2-cocycles, this was shown in work by the first author with Gillaspy, Norton, Reznikoff, and Wright. In this paper, we extend those results to general twists over étale groupoids. In particular, we prove that certain clopen subgroupoids of locally compact, Hausdorff, étale groupoids give rise to Cartan subalgebras in the twisted groupoid C*-algebra.