Abstract: We perform the canonical analysis of a dust thin shell coupled to (2+1)-dimensional gravity for different cosmological constants. Spacetime has a flat and BTZ black hole solution for zero and negative cosmological constant, respectively. The phase space turned out to be 𝐴𝐷𝑆2 space,
and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in noncommutativity in coordinate space and discreteness of the shell radius in the 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 the resolution of the problem of central singularity.