  On every split supermanifold equipped with the Rothstein even super-Poisson
bracket we construct a deformation quantization by means of a Fedosov-type
procedure. In other words, the supercommutative algebra of all smooth sections
of the dual Grassmann algebra bundle of an arbitrarily given vector bundle E
(equipped with a fibre metric) over a symplectic manifold M will be deformed by
a series of bidifferential operators having first order supercommutator
proportional to the Rothstein superbracket. Moreover, we discuss two
constructions related to the above result, namely the quantized BRST-cohomology
for a locally free Hamiltonian Lie group action (together with H.-C.Herbig and
S.Waldmann) and the classical BRST cohomology in the general coistropic (or
reducible) case without using a `ghosts of ghosts' scheme (together with
H.-C.Herbig).
