Mass-selected beams of atomic Ceq+ ions (q = 2, 3, 4), of C82+ and of endohedral Ce@C82+ ions were employed to study photoionization of free and encaged cerium atoms. The Ce 4d inner-shell contributions to single and double ionization of the endohedral Ce@C82+ fullerene have been extracted from the data and compared with expectations based on theory and the experiments with atomic Ce ions. Dramatic reduction and redistribution of the ionization contributions to 4d photoabsorption is observed. More than half of the Ce 4d oscillator strength appears to be diverted to the additional decay channels opened by the fullerene cage surrounding the Ce atom.