A model for two-dimensional (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 qua
ntum operators (SL(2, R) generators) lose their dynamical content (they are
no longer conjugated operators). The notion of spacetime itself in 2D grav
ity then arises as associated with this kinematical SL(2, R) symmetry. An e
nsemble of different copies of AdS do co-exist in this model with different
weights, depending on-their curvature (which is proportional to (h) over b
ar(2)) and they are connected by gravity operators. This model suggests tha
t, in general, quantum diffeomorphisms should not be imposed as constraints
to the theory, except for the classical limit.