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   <subfield code="a">We consider the four-band model of high-temperature superconductors with copper $$3d_{x^2 - y^2 } $$ and 4s electrons and oxygen 2p x and 2p y electrons. We assume that the Coulomb repulsion between the copper 3d electrons is strong. We diagonalize the oxygen subsystem and pass to the Wannier representation for the CuO 2 cluster. We study the properties of a local cell model and find its low-energy states such as the one-particle doublet and the two-particle singlet and triplet states. We consider the cell fermion delocalization because of their tunneling between the copper sites. We obtain a system of Dyson-type equations for renormalized one-particle Green's functions and discuss whether it can be simplified.</subfield>
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