We perform canonical analysis of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions.
The result is a reduced action depending on a finite number of degrees of freedom.
The emphasis is made on finding canonical variables providing the global chart for the entire phase space of the model.
It turns out that all the distinct pieces of momentum space could be assembled into a single manifold which has $ADS^2$-geometry, and the global chart for it is provided by the Euler angles.
In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point.
At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity. We also find the map between $ADS^2$ momentum space obtained here and momentum space in Kuchar variables, which could be helpful in extending the present results to 3+1 dimensions.