We present the results of an optical and near-infrared (NIR) monitoring campaign of the counterpart of Gamma-Ray Burst (GRB) 000911, located at redshift z=1.06, from 5 days to more than 13 months after explosion. Our extensive dataset is a factor of 2 larger and spans a time interval about 4 times longer than the ones considered previously for this GRB afterglow; this allows a more thorough analysis of its light curve and of the GRB host galaxy properties. The afterglow light curves show a single power-law temporal decline, modified at late times by light from a host galaxy with moderate intrinsic extinction, and possibly by an emerging supernova (SN). The afterglow evolution is interpreted within the classical fireball scenario as a weakly collimated adiabatic shock propagating in the interstellar medium. The presence of a SN light curve superimposed on the non-thermal afterglow emission is investigated: while in the optical bands no significant contribution to the total light is found from a SN, the NIR J-band data show an excess which is consistent with a SN as bright as the known hypernova SN1998bw. If the SN interpretation is true, this would be the farthest GRB-associated SN, as well as the farthest core-collapse SN, discovered to date. However, other possible explanations of this NIR excess are also investigated. Finally, we studied the photometric properties of the host, and found that it is likely to be a slightly reddened, subluminous, extreme starburst compact galaxy, with luminosity about 0.1 L*, an age of about 0.5 Gyr and a specific Star Formation Rate (SFR) of approximately 30 Msol yr-1 (L/L*)-1. This is the highest specific SFR value for a GRB host inferred from optical/NIR data.
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