CUNTZ-PIMSNER ALGEBRAS OF GROUP ACTIONS

We associate a *-bimodule over the group algebra to every self-similar group action on the space of one-sided sequences. Completions of the group algebra, which agree with the bimodule are investigated. This gives new examples of Hilbert bimodules and the associated Cuntz-Pimsner algebras. A direct proof of simplicity of these algebras is given. We show also a relation between the Cuntz algebras and the Higman-Thompson groups and define an analog of the Higman-Thompson group for the Cuntz-Pimsner algebra of a self-similar group action.