  We aim at characterizing the low-mass (sub)stellar population of the central
portion (2.4 pc$^2$) of the $\sim$2 Myr old cluster NGC 2244 using near
infrared spectroscopy. By studying this cluster, characterized by a low stellar
density and numerous OB stars, we aim at exploring the effect that OB stars may
have on the production of BDs. We obtain near infrared HK spectroscopy of 85
faint candidate members of NGC 2244. We derive the spectral type and extinction
by comparison with spectral templates. We evaluate cluster membership using
three gravity-sensitive spectral indices based on the shape of the $H$-band.
Furthermore, we evaluate the infrared excess from Spitzer of all the candidate
members of the cluster. Finally, we estimate the mass of all the candidate
members of the cluster and derive the initial mass function, star-to-BD number
ratio and disk fraction. The initial mass function is well represented by a
power law ($dN/dM \propto M^{-\alpha}$) below 0.4 $M_\odot$, with a slope
$\alpha$ = 0.7-1.1 depending on the fitted mass range. We calculate a
star-to-BD number ratio of 2.2-2.8. We find the low-mass population of NGC 2244
to be consistent with nearby star-forming regions, although it is at the
high-end of BD production. We find BDs in NGC 2244 to be on average closer to
OB stars than to low-mass stars, which could potentially be the first evidence
of OB stars affecting the formation of BDs. We find a disk fraction of all the
members with spectral type later than K0 of 39$\pm$9% which is lower than
typical values found in nearby star-forming regions of similar ages.
