SrTiO₃ (STO) is the most frequently used substrate material for complex oxide films. In this work, STO is explored as a buffer layer on piezoelectric pseudocubic Pb (Mg_1/3Nb_2/3) _0.72Ti_0.28O₃ (001) (PMN-PT) substrates, which serve to reversibly strain thin films. The STO buffer layer reduces the in-plane lattice parameter and allows for a better lattice matching to a broader range of thin film materials. STO films (30 nm) have been grown with epitaxial orientation on PMN-PT with an in-plane lattice parameter close to that of bulk STO. The substrate's rhombohedral domain structure has been imaged by atomic force microscopy. The related ferroelectric domain structure has been investigated by piezoresponse force microscopy. Within a domain, STO grows with a rather low roughness (rms<0.2 nm). The transfer of the piezoelectric substrate strain to the STO film and its variation with an applied electric field are studied using x-ray diffraction. The strain dependence of the electrical resistance is measured for a ferromagnetic manganite film grown on top of the STO. Both experiments confirm qualitatively that the STO buffer transfers the substrate strain into a functional film deposited on top.