The "unusual" isotope shift in high-temperature superconductors can be   explained by the usual theory of the electron-phonon interaction
  We show that recent ARPES results on the "unusual" oxygen isotope shift in the real part of the self-energy in the optimally doped $Bi2212$ samples can be qualitatively (and semi-quantitatively) explained by the theory of the electron-phonon interaction (EPI) elaborated few decades ago. However, for a quantitative analysis of the ARPES spectra it is necessary to know the momentum dependence of the EPI, the Coulomb contribution at high energies and the background due to impurities and defects. 
E. G. Maksimov, O. V. Dolgov and M. L. Kulic