  Context. In recent years, an in-depth gamma-ray analysis of the Orion region
has been carried out by the AGILE and Fermi-LAT (Large Area Telescope) teams
with the aim of estimating the H2-CO conversion factor, XCO. The comparison of
the data from both satellites with models of diffuse gamma-ray Galactic
emission unveiled an excess at (l,b)=[213.9, -19.5], in a region at a short
angular distance from the OB star k-Ori. Possible explanations of this excess
are scattering of the so-called "dark gas", non-linearity in the H2-CO
relation, or Cosmic-Ray (CR) energization at the k-Ori wind shock.
  Aims. Concerning this last hypothesis, we want to verify whether cosmic-ray
acceleration or re-acceleration could be triggered at the k-Ori forward shock,
which we suppose to be interacting with a star-forming shell detected in
several wavebands and probably triggered by high energy particles.
  Methods. Starting from the AGILE spectrum of the detected gamma-ray excess,
showed here for the first time, we developed a valid physical model for
cosmic-ray energization, taking into account re-acceleration, acceleration,
energy losses, and secondary electron contribution.
  Results. Despite the characteristic low velocity of an OB star forward shock
during its "snowplow" expansion phase, we find that the Orion gamma-ray excess
could be explained by re-acceleration of pre-existing cosmic rays in the
interaction between the forward shock of k-Ori and the CO-detected,
star-forming shell swept-up by the star expansion. According to our
calculations, a possible contribution from freshly accelerated particles is
sub-dominant with respect the re-acceleration contribution. However, a simple
adiabatic compression of the shell could also explain the detected gamma-ray
emission. Futher GeV and TeV observations of this region are highly recommended
in order to correctly identify the real physical scenario.
