  We consider a space-time with spatial sections isomorphic to the group
manifold of SU(2). Triad and connection fluctuations are assumed to be
SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform
non-perturbative path integral quantization of the model. Contarary to previous
claims the path integral measure appeared to be non-singular near
configurations admitting additional Killing vectors. In this model we are able
to calculate the generating functional of Green functions of the reduced phase
space variables exactly.
