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We consider a space-time with spatial sections isomorphic to the groupmanifold of SU(2). Triad and connection fluctuations are assumed to beSU(2)-invariant. Thus, they form a finite dimensional phase space. We performnon-perturbative path integral quantization of the model. Contarary to previousclaims the path integral measure appeared to be non-singular nearconfigurations admitting additional Killing vectors. In this model we are ableto calculate the generating functional of Green functions of the reduced phasespace variables exactly.Comment: 12 page

SU (2)-invariant reduction of (3+1)-dimensional Ashtekar gravity