Context. After the launch of the Swift satellite, the Gamma-Ray Burst (GRB) optical light-curve smoothness paradigm has been questioned thanks to the faster and better sampled optical follow-up, which has unveiled a very complex behaviour. This complexity is triggering the interest of the whole GRB community. The GROND multi-channel imager is used to study optical and near-infrared (NIR) afterglows of GRBs with unprecedented optical and near-infrared temporal and spectral resolution. The GRB 081029 has a very prominent optical rebrightening event and is an outstanding example of the application of the multi-channel imager to GRB afterglows. Aims. Here we exploit the rich GROND multi-colour follow-up of GRB 081029 combined with XRT observations to study the nature of late-time rebrightenings that appear in the optical-NIR light-curves of some GRB afterglows. Methods. We analyse the optical and NIR observations obtained with the seven-channel Gamma-Ray burst Optical and Near-infrared Detector (GROND) at the 2.2 m MPI/ESO telescope and the X-ray data obtained with the XRT telescope on board the Swift observatory. The multi-wavelength temporal and spectral evolution is discussed in the framework of different physical models. Results. The extremely steep optical and NIR rebrightening observed in GRB 081029 cannot be explained in the framework of the standard forward shock afterglow model. The absence of a contemporaneous X-ray rebrightening and the evidence of a strong spectral evolution in the optical-NIR bands during the rise suggest two separate components that dominate in the early and late-time lightcurves, respectively. The steepness of the optical rise cannot be explained even in the framework of the alternative scenarios proposed in the literature unless a late-time activity of the central engine is assumed.
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