  Aims. We use the IBIS/ISGRI telescope on-board INTEGRAL to measure the
position of the centroid of the 20-200 keV emission from the Crab region.
Methods. We find that the astrometry of the IBIS telescope is affected by the
temperature of the IBIS mask during the observation. After correcting for this
effect, we show that the systematic errors in the astrometry of the telescope
are of the order of 0.5 arcsec. In the case of the Crab nebula and several
other bright sources, the very large number of photons renders the level of
statistical uncertainty in the centroid smaller or comparable to this value.
Results. We find that the centroid of the Crab nebula in hard X-rays (20-40
keV) is shifted by 8.0 arcsec with respect to the Crab pulsar in the direction
of the X-ray centroid of the nebula. A similar shift is also found at higher
energies (40-100 and 100-200 keV). We observe a trend of decreasing shift with
energy, which can be explained by an increase in the pulsed fraction. To
differentiate between the contribution of the pulsar and the nebula, we divide
our data into an on-pulse and off-pulse sample. Surprisingly, the nebular
emission (i.e., off-pulse) is located significantly away from the X-ray
centroid of the nebula. Conclusions. In all 3 energy bands (20-40, 40-100, and
100-200 keV), we find that the centroid of the nebula is significantly offset
from the predicted position. We interpret this shift in terms of a cut-off in
the electron spectrum in the outer regions of the nebula, which is probably the
origin of the observed spectral break around 100 keV. From a simple
spherically-symmetric model for the nebula, we estimate that the electrons in
the external regions of the torus (d ~ 0.35 pc from the pulsar) reach a maximal
energy slightly below 10^14 eV.
