In this paper we combine archival and proprietary XMM-Newton observations (about 5deg^2) that overlap with the Sloan Digital Sky Survey to explore the nature of the moderate-z X-ray population. We focus on X-ray sources with optically red colours (g-r>0.4), which we argue are important for understanding the origin of the X-ray background. Firstly, these systems constitute a significant fraction, about 2/3, of the z<1 X-ray population to the limit f(2-8keV)~2e-14cgs. Secondly, their luminosity function under evolution of the form ~(1+z)^3 suggests that they could be responsible for about 17 per cent of the diffuse X-ray background to z=1. Thirdly, their stacked X-ray spectrum in the range 1-8keV is consistent with a power-law distribution with Gamma~1.4 (without fitting intrinsic absorption), i.e. similar to the diffuse X-ray background. We find that the optically red X-ray population comprises a mixed bag of objects, both obscured (N_H>1e22 cm^{-2}) and unobscured (N_H<1e22 cm^{-2}), with a wide range of X-ray luminosities up L_X~1e44cgs. We argue that dilution of the AGN light by the host galaxy may play a role in shaping the continuum optical emission of this population. Finally, we explore a possible association of these sources and the moderate-z red (J-Ks>2mag) AGNs identified in the Two Micron All Sky Survey (2MASS). The median N_H of the red X-ray sources studied here is ~1e21cm^{-2}, lower than that found for the 2MASS AGNs, suggesting different populations.
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