Groupoid Semidirect Product Fell Bundles I- Actions by Isomorphisms

TL;DR

This paper introduces a construction for semidirect-product Fell bundles under groupoid actions by isomorphisms and proves an isomorphism between its $C^{*}$-algebra and a crossed product, advancing the understanding of groupoid actions on Fell bundles.

Contribution

It develops a new framework for semidirect-product Fell bundles with isomorphism actions and establishes their $C^{*}$-algebra isomorphism to crossed products.

Findings

Construction of semidirect-product Fell bundles from groupoid actions

Proof of $C^{*}$-algebra isomorphism to crossed products

Extension of Fell bundle theory to actions by isomorphisms

Abstract

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.