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, \'etale 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 twisted C*-algebras of non-effective groupoids G can also possess Cartan subalgebras: In work by the first author together with Gillaspy, Norton, Reznikoff, and Wright, sufficient conditions on a subgroupoid S of G were found that ensure that S gives rise to a Cartan subalgebra in the cocycle-twisted C*-algebra of G. In this paper, we extend these results to general twists E, and we refine the conditions on the subgroupoid for C^*ᵣ(S;ES) to be a Cartan subalgebra of C^*ᵣ(G;E).