The　structural　properties　and　the　4f　-＞　5d　absorptions　of　Ce-doped　LuAlO3　have　been　studied　using　the　density　functional　theory-based　generalized　gradient　approximation　PBE　+　U　(PBE:　Perdew,　Burke　and　Ernzerhof)　and　wavefunction-based　embedded　cluster　calculations,　respectively.　The　PBE　or　PBE　+　U　calculations　reveal　that　the　substitution　of　Ce　for　Lu　induces　a　strongly　anisotropic　distortion　of　the　local　atomic　structure　around　the　dopant　site,　which　is　largely　insensitive　to　the　value　of　U　for　the　Ce　4f　states.　The　calculated　electronic　structures　depend　explicitly　on　the　value　of　U,　and　a　value　of　U　approximate　to　6　eV　is　determined　by　comparison　with　experimental　x-ray　photoelectron　data　for　CeAlO3.　On　the　basis　of　the　PBE-optimized　structure,　CASSCF/CASPT(2)　(complete-active-space　self-consistent-field/second-order　perturbation　theory)　embedded　cluster　calculations　for　the　Ce3+　C　4f　-＞　5d　transitions　yield　energy　and　intensity　patterns　in　fairly　good　agreement　with　those　estimated　from　the　experimental　absorption　spectrum.　A　Mulliken　spin　population　analysis　for　the　5d(1)　states　shows　that　the　origins　of　the　states　are　significantly　different　from　being　caused　by　the　cubic　crystal　field,　confirming　an　earlier　conclusion　as　regards　the　origin　of　the　5d(1)　states　based　on　semiempirical　molecular　orbital　calculations.　The　importance　of　spin-orbit　effects　on　the　energies　and　wavefunctions　of　the　Ce　5d(1)　states　is　highlighted.