  The method of the factorization of the path integral measure, based on a
nonlinear filtering equation, is extended to the case of a nonfree isometric
action of the compact semisimple unimodular Lie group on a smooth compact
Riemannian manifold. The method is applied to the path integral which describes
the "quantum" motion of the scalar particle on this manifold. The relation
between path integral representing the solution of the parabolic equation on
initial and reduced manifold is derived. It is shown that reduction reduction
leads to the non invariance of the path integral measure.
