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A recently developed formalism in which Kohn-Sham calculations are combinedwith an ``average pair density functional theory'' is reviewed, and some newproperties of the effective electron-electron interaction entering in thisformalism are derived. A preliminary construction of a fully self-consitentscheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th  International Workshop on Condensed Matter Theories

KOHN-SHAM CALCULATIONS COMBINED WITH AN AVERAGE PAIR-DENSITY FUNCTIONAL THEORY