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We perform canonical analysis of a model in which gravity is coupled to aspherically symmetric dust shell in 2+1 spacetime dimensions. The result is areduced action depending on a finite number of degrees of freedom. The emphasisis made on finding canonical variables providing the global chart for theentire phase space of the model. It turns out that all the distinct pieces ofmomentum space could be assembled into a single manifold which hasADS^{2}-geometry, and the global chart for it is provided by the Euler angles.This results in both non-commutativity and discreteness in coordinate space,which allows to resolve the central singularity. We also find the map betweenADS^{2} momentum space obtained here and momentum space in Kuchar variables,which could be helpful in extending the present results to 3+1 dimensions.

2+1-dimensional gravity coupled to a dust shell: quantization in terms of global phase space variables