  We present the results of the SDSS APOGEE INfrared Spectroscopy of Young
Nebulous Clusters program (IN-SYNC) survey of the Orion A molecular cloud. This
survey obtained high resolution near infrared (NIR) spectroscopy of about 2700
young pre-main sequence stars throughout the region, acquired across five
distinct fields spanning 6deg field of view (FOV). With these spectra, we have
measured accurate stellar parameters (T_eff, log g, v sin i) and extinctions,
and placed the sources in the Hertzsprung-Russel Diagram (HRD). We have also
extracted radial velocities for the kinematic characterization of the
population. We compare our measurements with literature results for a
sub-sample of targets in order to assess the performances and accuracy of the
survey. Source extinction shows evidence for dust grains that are larger than
those in the diffuse interstellar medium (ISM): we estimate an average R_V=5.5
in the region. Importantly, we find a clear correlation between HRD inferred
ages and spectroscopic surface-gravity inferred ages. This clearly indicates a
real spread of stellar radii at fixed temperature, and together with additional
correlations with extinction and with disk presence, strongly suggests a real
spread of ages large than a few Myr. Focussing on the young population around
NGC1980 iota Ori, which has previously been suggested to be a separate,
foreground, older cluster, we confirm its older (5Myr) age and low A_V, but
considering that its radial velocity distribution is indistinguishable from the
Orion A's population, we suggest that NGC1980 is part of Orion A's star
formation activity. Based on their stellar parameters and kinematic properties,
we identify 383 new candidate members of Orion A, most of which are diskless
sources in areas of the region poorly studied by previous works.
