  The field of the Gamma-Ray Burst GRB 040827 was observed with XMM-Newton and
with the ESO/VLT starting ~6 and ~12 hours after the burst, respectively. A
fading X-ray afterglow is clearly detected with the XMM-Newton/EPIC instrument,
with a time decay t^(-delta), with delta=1.41+/-0.10. Its spectrum is well
described by a power law (photon index Gamma=2.3+/-0.1) affected by an
absorption largely exceeding (by a factor ~5) the expected Galactic one,
requiring the contribution of an intrinsic, redshifted absorber. In the
optical/NIR range, the afterglow emission was observed in the Ks band, as a
weak source superimposed to the host galaxy, with magnitude Ks=19.44+/-0.13 (12
hours after the GRB, contribution from the host subtracted); in other bands the
flux is dominated by the host galaxy. Coupling constraints derived from X-ray
spectral fitting and from photometry of the host, we estimated a gas column
density in the range (0.4-2.6)x10^22 cm^-2 in the GRB host galaxy, likely
located at a redshift 0.5<z<1.7. GRB 040827 stands out as the best example of
an X-ray afterglow with intrinsic absorption.
