  We consider the covariant quantization of the D=11 massless superparticle
(M0-brane) in the spinor moving frame or twistor-like Lorentz harmonics
formulation. The action involves the set of 16 constrained 32 component
Majorana spinors, the spinor Lorentz harmonics parametrizing (as homogeneous
coordinates, modulo gauge symmetries) the celestial sphere S9. There presence
allows us to separate covariantly the first and the second class constraints of
the model. After taking into account the second class constraints by means of
Dirac brackets and after further reducing the first class constraints algebra,
the system is described in terms of a simple BRST charge associated to the d=1,
n=16 supersymmetry algebra. The study of the cohomology of this BRST operator
requires a regularization by complexifying the bosonic ghosts for the
kappa-symmetry and further reduction of the regularized cohomology problem to
the one for a simpler complex BRST charge which is essentially the pure spinor
BRST operator by Berkovits, but with a composite pure spinor. This exhibits a
possible origin of the complexity (non-hermiticity) characteristic of the
Berkovits pure spinor approach.
  The simple structure of the nontrivial cohomology of the M0-brane BRST charge
finds explanation in the properties that the superparticle action exhibits in
the so-called `covariantized light-cone' basis. The the covariant quantization
in this basis hints possible hidden symmetries of D=11 supergravity. Besides
SO(16), we discuss also some indirect arguments in favor of the possible E8
symmetry.
