The space experiment CoRoT has recently detected transits by a hot Jupiter across the disc of an active G7V star (CoRoT-Exo-2a) that can be considered as a good proxy for the Sun at an age of approximately 0.5 Gyr. We present a spot modelling of the optical variability of the star during 142 days of uninterrupted observations performed by CoRoT with unprecedented photometric precision. We apply spot modelling approaches previously tested in the case of the Sun by modelling total solar irradiance variations. To model the light curve of CoRoT-Exo-2a, we take into account both the photometric effects of cool spots as well as those of solar-like faculae, adopting solar analogy. Two active longitudes initially on opposite hemispheres are found on the photosphere of CoRoT-Exo-2a with a rotation period of 4.522 $pm$ 0.024 days. Their separation changes by approximately 80 degrees during the time span of the observations. From this variation, a relative amplitude of the surface differential rotation lower than about 1 percent is estimated. Individual spots form within the active longitudes and show an angular velocity about 1 percent smaller than that of the longitude pattern. The total spotted area shows a cyclic oscillation with a period of 28.9 $pm$ 4.3 days, which is close to 10 times the synodic period of the planet as seen by the rotating active longitudes. The implications of such results for the internal rotation of CoRoT-Exo-2a are discussed on the basis of solar analogy. A possible magnetic star-planet interaction is suggested by the cyclic variation of the spotted area. Alternatively, the 28.9-d cycle may be related to Rossby-type waves propagating in the subphotospheric layers of the star.
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