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Transverse momentum (pT) spectra of pions, kaons, and protons up to pT=20 GeV/c have been measured in Pb-Pb collisions at sNN−−−√=2.76 TeV using the ALICE detector for six different centrality classes covering 0-80%. The proton-to-pion and the kaon-to-pion ratios both show a distinct peak at pT≈3 GeV/c in central Pb-Pb collisions that decreases towards more peripheral collisions. For pT>10 GeV/c, the nuclear modification factor is found to be the same for all three particle species in each centrality interval within systematic uncertainties of 10-20%. This suggests there is no direct interplay between the energy loss in the medium and the particle species composition in the hard core of the quenched jet. For pT<10 GeV/c, the data provide important constraints for models aimed at describing the transition from soft to hard physics.