  Context: Grids of stellar models, computed with the same physical
ingredients, allow one to study the impact of a given physics on a broad range
of initial conditions and are a key ingredient for modeling the evolution of
galaxies. Aims: We present a grid of single star models for masses between 0.8
and 120 $M_\odot$, with and without rotation for a mass fraction of heavy
element Z=0.006, representative of the Large Magellanic Cloud (LMC). Methods:
We used the Geneva stellar evolution code. The evolution was computed until the
end of the central carbon-burning phase, the early asymptotic giant branch
phase, or the core helium-flash for massive, intermediate, and low mass stars,
respectively. Results: The outputs of the present stellar models are well
framed by the outputs of the two grids obtained by our group for metallicities
above and below the one considered here. The models of the present work provide
a good fit to the nitrogen surface enrichments observed during the main
sequence for stars in the LMC with initial masses around 15 $M_\odot$. They
also reproduce the slope of the luminosity function of red supergiants of the
LMC well, which is a feature that is sensitive to the time-averaged mass loss
rate over the red supergiant phase. The most massive black hole that can be
formed from the present models at Z=0.006 is around 55 $M_\odot$. No model in
the range of mass considered will enter into the pair-instability supernova
regime, while the minimal mass to enter the region of pair pulsation
instability is around 60 $M_\odot$ for the rotating models and 85 $M_\odot$ for
the nonrotating ones. Conclusions: The present models are of particular
interest for comparisons with observations in the LMC and also in the outer
regions of the Milky Way. We provide public access to numerical tables that can
be used for computing interpolated tracks and for population synthesis studies.
