The jets of GRS 1915+105 carry a considerable energy away from the central source into the interstellar medium (ISM). The similarity of the jets of this source and jets in radio galaxies or radio-loud quasars suggests that we should detect large-scale, synchrotron-emitting radio structures surrounding GRS 1915+105. However, these large structures have not been found. We show that by adapting a model for the radio lobes of extragalactic jet sources we predict a radio surface brightness of the equivalent structures of GRS 1915+105 below the current detection limits. The model uses an energy transport rate of the jets averaged over the jet lifetime. This transport rate is found to be considerably lower than the power of the jets during the rare major ejection events. Thus, the lobes contain less energy than would be inferred from these events and produce a lower radio luminosity. The model also predicts a lifetime of the jets of order 106 yr and a gas density of the ISM in the vicinity of GRS 1915+105 of ~150 cm-3. The impact sites of the jets are identified with two IRAS regions with a flat radio spectrum located on either side of GRS 1915+105. Observations of molecular lines and dust emission from these objects are consistent with our interpretation. Distance estimates for the IRAS regions give 6.5 kpc, and our model implies that this is also the distance to GRS 1915+105. This low distance estimate in combination with the observed motions of jet ejections on small scales yields a jet velocity of about 0.7c and an angle of 53° of the jets to our line of sight.