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By undertaking deep long-slit spectroscopy with the focal reducer SCORPIO of the Russian 6m telescope, we studied stellar population properties and their variation with radius in 15 nearby S0 galaxies sampling a wide range of luminosities and environments. For the large-scale stellar disks of S0s, we have measured SSP-equivalent metallicities ranging from the solar one down to [Z/H]=-0.4 - -0.7, rather high magnesium-to-iron ratios, [Mg/Fe] > +0.2, and mostly old SSP-equivalent ages. Nine of 15 (60%) galaxies have large-scale stellar disks older than 10 Gyr, and among those we find all the galaxies which reside in denser environments. The isolated galaxies may have intermediate-age stellar disks which are 7-9 Gyr old. Only two galaxies of our sample, NGC 4111 and NGC 7332, reveal SSP-equivalent ages of their disks of 2-3 Gyrs. Just these two young disks appear to be thin, while the other, older disks have scale heights typical for thick stellar disks. The stellar populations in the bulges at radii of 0.5r_eff are on the contrary more metal-rich than the solar metallicity, with the ages homogeneously distributed between 2 and 15 Gyr, being almost always younger than the disks. We conclude that S0 galaxies could not form in groups at z=0.4 as is thought now; a new scenario of the general evolution of disk galaxies is proposed instead., Accepted to the MNRAS