  We perform quantization of a model in which gravity is coupled to a circular
dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum
space of this model is ADS^2-space, 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.
