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We consider groupoids on $\{1,2,..,d\}^\mathbb{N}$, cocycles and the countingmeasure as transverse function. We generalize results relating quasi-invariantprobabilities with eigenprobabilities for the dual of the Ruelle operator. Weassume a mild compatibility of the groupoid with the symbolic structure. Wepresent a generalization of the Ruelle operator - the Haar-Ruelle operator -taking into account the Haar structure. We consider continuous and alsoH\"older cocycles. IFS with weights appears in our reasoning in the H\"oldercase.

Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator