  A model for 2D Quantum Gravity is constructed out of the Virasoro group. To
this end the quantization of the abstract Virasoro group is revisited. For the
critical values of the conformal anomaly c, some quantum operators (SL(2,R)
generators) lose their dynamical content (they are no longer conjugated
operators). The notion of space-time itself in 2D gravity then arises as
associated with this kinematical SL(2,R) symmetry. An ensemble of different
copies of AdS do co-exist in this model with different weights, depending on
their curvature (which is proportional to \hbar^{2}) and they are connected by
gravity operators. This model suggests that, in general, quantum diffemorphisms
should not be imposed as constraints to the theory, except for the classical
limit.
