Isobaric single charge-exchange reactions, changing nuclear charges by one unit but leaving the mass partitions unaffected, have been for the first time investigated by peripheral collisions of 112Sn ions accelerated up to 1A GeV at the GSI facilities. The high-resolving power of the FRS spectrometer allows us to obtain (p,n)-type isobaric charge-exchange cross sections with an uncertainty of 3.5% and to separate quasi-elastic and inelastic components in the missing-energy spectra of the ejectiles. The inelastic component is associated to the excitation of the Δ(1232) isobar resonance and the emission of pions in s-wave both in the target and projectile nucleus, while the quasi-elastic contribution is associated to the nuclear spin-isospin response of nucleon-hole excitations. An apparent shift of the Δ-resonance peak of ∼63 MeV is observed when comparing the missing-energy spectra obtained from the measurements with proton and carbon targets. A detailed analysis, performed with a theoretical model for the reactions, indicates that this observation can be simply interpreted as a change in the relative magnitude between the contribution of the excitation of the resonance in the target and in the projectile.