  We interpret the Cuntz-Pimsner covariance condition as a nondegeneracy
condition for representations of product systems. We show that Cuntz-Pimsner
algebras over Ore monoids are constructed through inductive limits and section
algebras of Fell bundles over groups. We construct a groupoid model for the
Cuntz-Pimsner algebra coming from an action of an Ore monoid on a space by
topological correspondences. We characterise when this groupoid is effective or
locally contracting and describe its invariant subsets and invariant measures.
