Context. Light bridges are convective intrusions in sunspots that often show enhanced chromospheric activity. Aims: We seek to determine the nature of flux emergence in a light bridge and the processes related to its evolution in the solar atmosphere. Methods: We analyse a sequence of high-resolution spectropolarimetric observations of a sunspot taken at the Swedish 1-m Solar Telescope. The data consist of spectral scans of the photospheric Fe i line pair at 630 nm and the chromospheric Ca ii 854.2 nm line. Bisectors were used to construct Dopplergrams from the Fe i 630.15 nm measurements. We employed LTE and non-LTE inversions to derive maps of physical parameters in the photosphere and chromosphere, respectively. Results: We observe the onset of blueshifts of about 2 km s-1 near the entrance of a granular light bridge on the limbward side of the spot. The blueshifts lie immediately next to a strongly redshifted patch that appeared six minutes earlier. Both patches can be seen for 25 min until the end of the sequence. The blueshifts coincide with an elongated emerging granule, while the redshifts appear at the end of the granule. In the photosphere, the development of the blueshifts is accompanied by a simultaneous increase in field strength of about 400 G. The field inclination increases by some 25°, becoming nearly horizontal. At the position of the redshifts, the magnetic field is equally horizontal but of opposite polarity. An intense brightening is seen in the Ca ii filtergrams over the blueshifts and redshifts, about 17 min after their detection in the photosphere. The brightening is due to emission in the blue wing of the Ca ii 854.2 nm line, close to its knee. Non-LTE inversions reveal that this kind of asymmetric emission is caused by a temperature enhancement of ~700 K between -5.0 ≤ log τ ≤ -3.0 and a blueshift of 3 km s-1 at log τ = -2.3 that decreases to zero at log τ = -6.0 Conclusions: The photospheric blueshifts and redshifts observed in a granular light bridge seem to be caused by the emergence of a small-scale, flat Ω-loop with highly inclined footpoints of opposite polarity that brings new magnetic field to the surface. The gas motions detected in the two footpoints are reminiscent of a siphon flow. The rising loop is probably confined to the lower atmosphere by the overlying sunspot magnetic field and the interaction between the two flux systems may be responsible for temperature enhancements in the upper photosphere/lower chromosphere. This is the first time that magnetic flux is observed to emerge in the strongly magnetised environment of sunspots, pushed upwards by the convective flows of a granular light bridge. The movie associated to Fig. 2 is available in electronic form at http://www.aanda.org