# Journal of Operator Theory

Volume 89, Issue 1, Winter 2023  pp. 125-153.

Groupoid semidirect product Fell bundles. I. Actions by isomorphisms

Authors:  Lucas Hall (1), S. Kaliszewski (2), John Quigg (3), Dana P. Williams (4)
Author institution: (1) School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, U.S.A.
(2) School of Mathematical and Statistical Sciences,\break Arizona State University, Tempe, Arizona 85287, U.S.A.
(3) School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, U.S.A.
(4) Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755, U.S.A.

Summary: Given an action of a groupoid by isomorphisms on a Fell bundle (over another groupoid), we form a semidirect product Fell bundle, and prove that its $C^*$-algebra is isomorphic to a crossed product.

DOI: http://dx.doi.org/10.7900/jot.2021may05.2349
Keywords: groupoid, Fell bundle, $C^*$-algebra, groupoid crossed product