@article{Qiang2026, 
author = {Xiangqi Qiang},
title = {Continuous orbit equivalence of groupoid actions},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {13287-13303},
keywords = {groupoid action, transformation groupoid, continuous orbit equivalence, conjugacy, groupoid C∗-algebra},
url = {https://www.sciopen.com/article/10.3934/math.2026548},
doi = {10.3934/math.2026548},
abstract = {In this paper, I studied continuous actions of étale groupoids on compact Hausdorff spaces and the associated operator algebras. I introduced notions of conjugacy and continuous orbit equivalence for such groupoid actions and characterized them in terms of the corresponding transformation groupoids and their reduced        C    ∗  -algebras. In particular, I proved that two topologically free actions are continuously orbit equivalent if and only if their associated transformation groupoid        C    ∗  -algebras are isomorphic, and if and only if there exists a        C    ∗  -algebra isomorphism preserving the canonical Cartan subalgebras between the corresponding reduced        C    ∗  -algebras of these transformation groupoids.}
}