  We propose a microscopic theory of superconductivity for systems with strong
electron correlations such as cuprates in the framework of the extended Hubbard
model where the intersite Coulomb repulsion and electron-phonon interaction are
taken into account. The Dyson equation for the normal and pair Green functions
for the Hubbard operators (HOs) is derived. Due to the unconventional
commutation relations for the HOs, a specific kinematical interaction of
electrons with spin and charge fluctuations with a large coupling constant of
the order of the kinetic energy of electrons $W$ emerges that results in the
$d$-wave pairing with high-$T_c$. Superconductivity can be suppressed only for
a large intersite Coulomb repulsion $V > W$. Isotope effect on $T_c$ caused by
electron-phonon interaction is weak at optimal doping and increases at low
doping. The kinematical interaction is absent in the spin-fermion models and is
lost in the slave-boson (-fermion) models treated in the mean-field
approximation.
