In this Letter, we investigate the time delay of photoelectrons by fullerenes shell in endohedrals. We present general formulas in the frame of the random phase approximation with exchange (RPAE) applied to endohedrals A@CN that consist of an atom A located inside of a fullerenes shell constructed of N carbon atoms C. We calculate the time delay of electrons that leave the inner atom A in course of A@CN photoionization. Our aim is to clarify the role that is played by CN shell. As concrete examples of A we have considered Ne, Fr, Kr and Xe, and as fullerene we consider C60. The presence of the C60 shell manifests itself in powerful oscillations of the time delay of an electron that is ionized from a given subshell nl by a photon with energy. Calculations are performed for outer, subvalent and d-subshells.
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