We present calculated cross sections for elastic and inelastic collisions of low-energy electrons with octafluorocyclobutane, c-C4F8. The integral elastic cross section displays a rich resonance structure, which we analyze in terms of temporary trapping in virtual valence orbitals. The differential elastic cross sections compare well with recent measurements at energies where the approximations used in the calculations are expected to be valid. Integral and differential cross sections for electron-impact excitation of the lowest singlet and triplet excited states were obtained. We relate the small magnitude of the inelastic integral cross sections and the unusual form of the inelastic differential cross sections to the symmetries of the electronic states involved in the transition.