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We characterize Cuntz-Nica-Pimsner algebras for compactly aligned productsystems over quasi-lattice ordered groupoids. We show that the full crosssectional $C^*$-algebras of Fell bundles of Morita equivalence bimodules areisomorphic to the related Cuntz-Nica-Pimsner algebras under certain conditions.

Cuntz-Nica-Pimsner algebras associated to product systems over quasi-lattice ordered groupoids