  Source I in the Orion-KL nebula is believed to be the nearest example of a
massive star still in the main accretion phase. It is thus one of the best
cases for studying the properties of massive protostars to constrain high-mass
star formation theories. Near-infrared radiation from source I escapes through
the cavity opened by the OMC1 outflow and is scattered by dust towards our line
of sight. The reflected spectrum offers a unique possibility of observing the
emission from the innermost regions of the system and probing the nature of
source I and its immediate surroundings. We obtained moderately high
spectral-resolution (R~9000) observations of the near-infrared diffuse emission
in several locations around source I/Orion-KL. We observed a widespread rich
absorption line spectrum that we compare with cool stellar photospheres and
protostellar accretion disk models. The spectrum is broadly similar to strongly
veiled, cool, low-gravity stellar photospheres in the range Teff~3500-4500 K,
luminosity class I-III. An exact match explaining all features has not been
found, and a plausible explanation is that a range of different temperatures
contribute to the observed absorption spectrum. The 1D velocity dispersions
implied by the absorption spectra, sigma~30 km/s, can be explained by the
emission from a disk around a massive, mstar~10 Msun, protostar that is
accreting at a high rate, mdot~3x10^{-3} Msun/yr. Our observations suggest that
the near-infrared reflection spectrum observed in the Orion-KL region is
produced close to source I and scattered to our line of sight in the OMC1
outflow cavity. The spectrum allows us to exclude source I being a very large,
massive protostar rotating at breakup speed. We suggest that the absorption
spectrum is produced in a disk surrounding a ~10 Msun protostar, accreting from
its disk at a high rate of a few 10^{-3} Msun/yr.
