A stabilization theorem for Fell bundles over groupoids

  title={A stabilization theorem for Fell bundles over groupoids},
  author={Marius Ionescu and Alex Kumjian and Aidan Sims and Dana P. Williams},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  pages={79 - 100}
We study the C *-algebras associated with upper semi-continuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer–Raeburn ‘stabilization trick’, we construct from each such bundle a groupoid dynamical system whose associated Fell bundle is equivalent to the original bundle. The upshot is that the full and reduced C *-algebras of any saturated upper semi-continuous Fell bundle are stably isomorphic to the full and reduced crossed products of an… 

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