In this letter, fabrication of all-epitaxial GeSn-on-insulator (GeSnOI) heterostructures is investigated, wherein both the GeSn epilayer and the Gd2O3 insulator are grown on Si(111) substrates by conventional molecular beam epitaxy. Analysis of the crystal and surface quality by high-resolution X-ray diffraction, cross-sectional transmission electron microscopy, and atomic force microscopy reveals the formation of a continuous and fullyrelaxed single-crystalline GeSn epilayer (with a root-mean-square surface roughness of 3.5 nm), albeit GeSn epitaxy on Gd2O3 initiates in the Volmer-Weber growth mode. The defect structure of the GeSn epilayers is dominated by stacking faults and reflection microtwins, which are formed during the coalescence of the initiallyformed islands. The concentration and mobility of holes, introduced by un-intentional p-type doping of the GeSn epilayers, were estimated to 8 × 10 16 cm -3 and 176 cm -2 V -1 s -1 , respectively. In metal-semiconductor-metal Schottky diodes, fabricated with these GeSnOI heterostructures, the dark current was observed to be lower by a decade, when compared to similar diodes fabricated with GeSn/Ge/Si(001) heterostructures. The results presented here are thus promising for the development of these engineered substrates for (opto-)electronic applications.