  In the last years ample experimental evidence has shown that charge carriers
in high-temperature superconductors are strongly correlated but also coupled
with lattice vibrations (phonons), signaling that the true origin of high-Tc
superconductivity can only be found in a proper combination of Coulomb and
electron-phonon interactions. On this basis, we propose and study a model for
high-Tc superconductivity, which accounts for realistic Coulomb repulsion,
strong electron-phonon (Fr\"ohlich) interaction and residual on-site (Hubbard
\tilde{U}) correlations without any ad-hoc assumptions on their relative
strength and interaction range. In the framework of this model, which exhibits
a phase transition to a superconducting state with a critical temperature Tc
well in excess of 100K, we emphasize the role of \tilde{U} as the driving
parameter for a BEC/BCS crossover. Our model lays a microscopic foundation for
the polaron-bipolaron theory of superconductivity. We argue that the high-Tc
phenomenon originates in competing Coulomb and Fr\"ohlich interactions beyond
the conventional BCS description.
