  We perform canonical analysis of an action in which 2+1-dimensional gravity
with negative cosmological constant is coupled to cylindrically symmetric dust
shell. The resulting phase space is finite dimensional having geometry of SO(2;
2) group manifold. Representing the Poisson brackets by commutators results in
the algebra of observables which is a quantum double D(SL(2)q). Deformation
parameter q is real when the total energy of the system is below the threshold
of a black hole formation, and a root of unity when it is above. Inside the
black hole the spectra of the shell radius and time operator are discrete and
take on a finite set of values. The Hilbert space of the black hole is thus
finite-dimensional.
