  We show that the so-called kinks and waterfalls observed in angle-resolved
photoemission spectra of La2-xSrxCuO4, a prototypical high-Tc superconducting
cuprate, result from the coupling of quasiparticles with two distinct nearly
critical collective modes with finite characteristic wave vectors, typical of
charge and spin fluctuations near a stripe instability. Both phonon-like charge
and spin collective modes are needed to account for the kinked quasiparticle
dispersions. This clarifies the long-standing question whether kinks are due to
phonons or spin waves and the nature of the bosonic mediators of the
electron-electron effective interaction in La2-xSrxCuO4.
