  In the canonical quantization of gravity in terms of the Ashtekar variables
one uses paths in the 3-space to construct the quantum states. Usually, one
restricts oneself to families of paths admitting only finite number of isolated
intersections. This assumption implies a limitation on the diffeomorphisms
invariance of the introduced structures. In this work, using the previous
results of Baez and Sawin, we extend the existing results to a theory admitting
all the possible piecewise smooth finite paths and loops. In particular, we
$(i)$ characterize the spectrum of the Ashtekar-Isham configuration space,
$(ii)$ introduce spin-web states, a generalization of the spin-network states,
$(iii)$ extend the diffeomorphism averaging to the spin-web states and derive a
large class of diffeomorphism invariant states and finally $(iv)$ extend the
3-geometry operators and the Hamiltonian operator.
