  We consider groupoids on $\{1,2,..,d\}^\mathbb{N}$, cocycles and the counting
measure as transverse function. We generalize results relating quasi-invariant
probabilities with eigenprobabilities for the dual of the Ruelle operator. We
assume a mild compatibility of the groupoid with the symbolic structure. We
present a generalization of the Ruelle operator - the Haar-Ruelle operator -
taking into account the Haar structure. We consider continuous and also
H\"older cocycles. IFS with weights appears in our reasoning in the H\"older
case.
