Groupoid Fell bundles for product systems over quasi-lattice ordered groups

@article{Rennie2015GroupoidFB,
  title={Groupoid Fell bundles for product systems over quasi-lattice ordered groups},
  author={Adam Graham Rennie and David I. Robertson and Aidan Sims},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2015},
  volume={163},
  pages={561 - 580}
}
Abstract Consider a product system over the positive cone of a quasi-lattice ordered group. We construct a Fell bundle over an associated groupoid so that the cross-sectional algebra of the bundle is isomorphic to the Nica–Toeplitz algebra of the product system. Under the additional hypothesis that the left actions in the product system are implemented by injective homomorphisms, we show that the cross-sectional algebra of the restriction of the bundle to a natural boundary subgroupoid… 

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