  We introduce a reduced model for a real sector of complexified Ashtekar
gravity that does not correspond to a subset of Einstein's gravity but for
which the programme of canonical quantization can be carried out completely,
both, via the reduced phase space approach or along the lines of the algebraic
quantization programme.\\ This model stands in a certain correspondence to the
frequently treated cylindrically symmetric waves.\\ In contrast to other models
that have been looked at up to now in terms of the new variables the reduced
phase space is infinite dimensional while the scalar constraint is genuinely
bilinear in the momenta.\\ The infinite number of Dirac observables can be
expressed in compact and explicit form in terms of the original phase space
variables.\\ They turn out, as expected, to be non-local and form naturally a
set of countable cardinality.
