  The CoRoT satellite has recently discovered a hot Jupiter that transits
across the disc of a F9V star called CoRoT-6 with a period of 8.886 days. We
model the photospheric activity of the star and use the maps of the active
regions to study stellar differential rotation and the star-planet interaction.
We apply a maximum entropy spot model to fit the optical modulation as observed
by CoRoT during a uninterrupted interval of about 140 days. Photospheric active
regions are assumed to consist of spots and faculae in a fixed proportion with
solar-like contrasts. Individual active regions have lifetimes up to 30-40
days. Most of them form and decay within five active longitudes whose different
migration rates are attributed to the stellar differential rotation for which a
lower limit of \Delta \Omega / \Omega = 0.12 \pm 0.02 is obtained. Several
active regions show a maximum of activity at a longitude lagging the
subplanetary point by about 200 degrees with the probability of a chance
occurrence being smaller than 1 percent. Our spot modelling indicates that the
photospheric activity of CoRoT-6 could be partially modulated by some kind of
star-planet magnetic interaction, while an interaction related to tides is
highly unlikely because of the weakness of the tidal force.
