  Applying a continuous-time quantum Monte-Carlo algorithm we calculate the
exact coherent band dispersion and the density of states of a two dimensional
lattice polaron in the region of parameters where any approximation might fail.
We find an isotope effect on the band structure, which is different for
different wave-vectors of the Brillouin zone and depends on the radius and
strength of the electron-phonon interaction. An isotope effect on the electron
spectral function is also discussed.

Superconductivity;Strongly Correlated Electrons