Gauge-invariant uniqueness theorems for P-graphs

We prove a version of the result in the title that makes use of maximal coactions in the context of discrete groups. Earlier Gauge-Invariant Uniqueness theorems for C^*-algebras associated to P-graphs and similar C^*-algebras exploited a property of coactions known as normality. In the present paper, the view point is that maximal coactions provide a more natural starting point to state and prove such uniqueness theorems. A byproduct of our approach consists of an abstract characterization of co-universal representations for a Fell bundle over a discrete group.