In conventional superconductors, the electron pairing that allows superconductivity is caused by exchange of virtual phonons, which are quanta of lattice vibration. For high-transition-temperature (high-T(c)) superconductors, it is far from clear that phonons are involved in the pairing at all. For example, the negligible change in T(c) of optimally doped Bi2Sr2CaCu2O8+delta (Bi2212; ref. 1) upon oxygen isotope substitution (16O --> 18O leads to T(c) decreasing from 92 to 91 K) has often been taken to mean that phonons play an insignificant role in this material. Here we provide a detailed comparison of the electron dynamics of Bi2212 samples containing different oxygen isotopes, using angle-resolved photoemission spectroscopy. Our data show definite and strong isotope effects. Surprisingly, the effects mainly appear in broad high-energy humps, commonly referred to as 'incoherent peaks'. As a function of temperature and electron momentum, the magnitude of the isotope effect closely correlates with the superconducting gap--that is, the pair binding energy. We suggest that these results can be explained in a dynamic spin-Peierls picture, where the singlet pairing of electrons and the electron-lattice coupling mutually enhance each other.