A deformation of the wave equation on a two-dimensional black hole is
considered as a toy-model for possible gravitational or stringy nonlocal
effects. The deformed wave-equation allows for an initial-value problem despite
being nonlocal. The classical singularity present in the classical geometry is
resolved by the deformation, so that propagation of a wave-packet can be
continued through the classically singular region, ultimately reaching another
asymptotically ``flat'' region.Comment: 12 pager, Latex with eepic macros, minor change
