  We show that the right-handed (RH) sneutrino in the NMSSM can account for the
observed excess in the Fermi-LAT spectrum of gamma rays from the Galactic
Centre, while fulfilling all the current experimental constraints from the LHC
as well as from direct and indirect dark matter searches. We have explored the
parameter space of this scenario, computed the gamma ray spectrum for each
phenomenologically viable solution and then performed a chi^2 fit to the
excess. Unlike previous studies based on model independent interpretations, we
have taken into account the full annihilation spectrum, without assuming pure
annihilation channels. Furthermore, we have incorporated limits from direct
detection experiments, LHC bounds and also the constraints from Fermi-LAT on
dwarf spheroidal galaxies (dSphs) and gamma ray spectral lines. In addition, we
have estimated the effect of the most recent Fermi-LAT reprocessed data (Pass
8). In general, we obtain good fits to the GCE when the RH sneutrino
annihilates mainly into pairs of light singlet-like scalar or pseudoscalar
Higgs bosons that subsequently decay in flight, producing four-body final
states and spectral features that improve the goodness of the fit at large
energies. The best fit (chi^2=20.8) corresponds to a RH sneutrino with a mass
of 64 GeV which annihilates preferentially into a pair of light singlet-like
pseudoscalar Higgs bosons (with masses of order 60 GeV). Besides, we have
analysed other channels that also provide good fits to the excess. Finally, we
discuss the implications for direct and indirect detection searches paying
special attention to the possible appearance of gamma ray spectral features in
near future Fermi-LAT analyses, as well as deviations from the SM-like Higgs
properties at the LHC. Remarkably, many of the scenarios that fit the GCE can
also be probed by these other complementary techniques.
