I wonder to what degree Interpol agents can take part in the pursuit of an international fugitive. The whole reason Interpol exists is precisely because one country's authorities cannot simply pursue their country's criminals in other countries, generally speaking.
Interpol is international however, presumably meaning their agents can indeed pursue criminals in any of its member countries, right? Well, I don't know; perhaps Interpol's role is merely as a middle man between different countries' law enforcements? How limited is their authority? I understand if this varies greatly, though any general info would be appreciated, and referrals to where one might find out the specific details regarding Interpol's authority in different countries.
So, what can Interpol agents do in different countries when pursuing an international criminal?