We present the results of a series of numerical simulations aimed to study the evolution of a disc galaxy within the global tidal field of a group environment. Both the disc galaxy and the group are modelled as multicomponent, collisionless, N-body systems, composed of both dark matter and stars. In our simulations, the evolution of disc galaxies is followed after they are released from the group virial radius, and as their orbits sink towards the group centre, under the effect of dynamical friction. We explore a broad parameter space, covering several aspects of the galaxy-group interaction that are potentially relevant to galaxy evolution. Namely, prograde and retrograde orbits, orbital eccentricities, disc inclination, role of a central bulge in discs, internal disc kinematics and galaxy-to-group mass ratios. We find that significant disc transformations occur only after the mean density of the group, measured within the orbit of the galaxy, exceeds ∼0.3–1 times the central mean density of the galaxy. The morphological evolution of discs is found to be strongly dependent on the initial inclination of the disc with respect to its orbital plane, i.e. discs on face-on and retrograde orbits are shown to retain their disc structures and kinematics longer, in comparison to prograde discs. This suggests that after interacting with the global tidal field alone, a significant fraction of disc galaxies should be found in the central regions of groups. Prominent central bulges are not produced, and pre-existing bulges are not enhanced in discs after the interaction with the group. Assuming that most S0 are formed in group environments, this implies that prominent bulges should be formed mostly by young stars, created only after a galaxy has been accreted by a group. Finally, contrary to some current implementations of tidal stripping in semi-analytical models of galaxy evolution, we find that more massive galaxies suffer more tidal stripping. This is because dynamical friction brings them faster to the group centre, in comparison to their lower mass counterparts.