  We study the effects of the rippling of the graphene sheet on the
quasiparticle dispersion. This is achieved using a generalization to the
honeycomb lattice of the Momentum Average approximation, which is accurate for
all coupling strengths and at all energies. We show that even though the
position of the Dirac points may move and the Fermi speed can be renormalized
significantly, quasiparticles with very long lifetimes survive near the Dirac
points even for very strong couplings.
