A quick note about Jurisdiction, for some who only know the term from movies.
Jurisdiction has three main levels of how it applies:
Personal: Jurisdiction over a person/people no matter where they are, usually used in military law or to apprehend fugitives who have committed a crime in another country (extradition being another, trickier matter)
Territorial: Legal command over a certain geographic area with usually strict boundaries. This means that the people in this area and any events that occur in it fall under the legal purview of the legal body(ies) granted authority over the aforementioned area. This is why a crime committed in, say, New York City can be prosecuted or pursued when the suspect/felon has left the original jurisdiction. Note that after crossing state or country borders, territorial will blur with personal in terms of how the process is negotiated.
Universal Jurisdiction: Universal is reserved for the highest level of criminal acts and or threats. Those who authorize/attempt/commit genocide, large scale human or drug trafficking, arms dealing and incredibly heinous crimes are considered under the jurisdiction of any country which apprehends them or gets them first. These individuals are usually tried in the Hague or World Court, since their crimes are on a level to effect multiple countries or people.
Interpol usually only acts on either a criminal dispute that involves three or more member countries (arms trafficking, drug trade, human trafficking, sometimes human smuggling). Even then INTERPOL is STILL bound by both their own laws as a technically neutral third party and the laws of the country in which they are seeking to obtain their suspect of felon. This means that an INTERPOL agent who apprehends a Columbian drug lord in America will have to A) Dispute proper jurisdiction with the nation's authorities (the FBI in this case and the US Attorney's Office) and abide by the nation's laws of detainment until the matter is settled.