We present the results of deep near-infrared observations of 11 hard X-ray selected sources in the Hellas2XMM survey, with faint optical magnitude (R>24) and high X-ray-to-optical flux ratio. All but one of the sources have been detected in the Ks band, with bright counterparts (Ks<19) and red colors (R-K>5), and therefore belong to the ERO population. A detailed analysis of the surface brightness profiles allows us to classify all of the NIR counterparts. There are 2 point-like objects, 7 elliptical galaxies and one source with a disky profile. None of the extended sources shows any evidence for the presence of a central unresolved object tracing the putative X-ray emitting AGN. Using both the R-K colors and the morphological information, we have estimated for all the sources a ``minimum photometric redshift, ranging between 0.8 and 2.4; the elliptical hosts have zmin=0.9-1.4. We computed the X-ray properties using these redshifts: most of the sources have NH>10^{22}, with unabsorbed X-ray luminosities up to 10^{45}erg s^{-1}. These objects therefore belong to the population of obscured (Type II) quasars and, from a statistical point of view, they turn out to be a non-negligible fraction (~10%) of the most luminous AGN. Selecting the high X/O sources for a follow-up study in the NIR is therefore a powerful technique aimed at studying at high redshift the hosts of Type II AGN. Overall, our results seem to indicate that the hosts are mostly elliptical galaxies at z~1, and that these near-IR bright objects would be among the most massive spheroids at these epochs.
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