  We present an {\it ab initio} many-body GW calculation of the self-energy,
the quasiparticle band plot and the spectral functions in free-standing undoped
graphene. With respect to other approaches, we numerically take into account
the full ionic and electronic structure of real graphene and we introduce
electron-electron interaction and correlation effects from first principles.
Both non-hermitian and also dynamical components of the self-energy are fully
taken into account. With respect to DFT-LDA, the Fermi velocity is
substantially renormalized and raised by a 17%, in better agreement with
magnetotransport experiments. Furthermore, close to the Dirac point the linear
dispersion is modified by the presence of a kink, as observed in ARPES
experiments. Our calculations show that the kink is due to low-energy $\pi \to
\pi^*$ single-particle excitations and to the $\pi$ plasmon. Finally, the GW
self-energy does not open the band gap.
