Well, the authority of Longbow is actually being hotly debated. Bring it up in the City Life section and you'll see the thread flare up brightly, mostly by heavy-villain-side players, with personal opinions and some research based on Paragon Wiki.
On that note... Paragon Wiki
Now, from my experience, Freedom Corps and Longbow are an experiment. Think of the sister organizations as being the beginning of an organization similar to Marvel's S.H.I.E.L.D. However, not every nation in the world is beholden to NATO's laws, nor are many of the nations of the world very keen on a foreign entity's authority (in my opinion, this is the reason why the United Nations is so heavily hamstrung, even by its most powerful member nations; nobody likes being told how to play in their own sandbox). So Longbow works more as a limited emergency enforcement force. The only way they can officially operate in the Rogue Isles, for instance, is if they can prove that something is world-threatening enough to warrant their involvement. Apparently, officially, Arachnos and Longbow are working together to maintain the peace of the Rogue Isles (due to the massive numbers of renegade super-powered threats), though the opposite is so obviously the case.
At least, that's how I rationalize the Agincourt Fortress being in the middle of the Nerva Archipelago.
As far as Freedom Corps' capabilities in Paragon City, they do not have authority over anything, but can request jurisdiction from the mayor's office or other proper authorities in certain situations (just like the FBI, DHS, or ATF have to; the cliche is that the municipality usually grants such authority with a stamp, so people often have the mistaken impression that the FBI and other such organizations can simply brush aside local police). Since the PPD is still replenishing itself (they don't like needing to use those drones, but the officers they've got are mostly rookies), the PPD is usually all-too-ready to cede control of a situation over to the F.C., which is usually gracious enough to be polite about it.
Normally, the F.C. is treated as a super-powered SWAT team. They hardly ever investigate situations, but there are some notable exceptions (do the Faultline/Overbrook arcs, especially Agent G's portion). Normally, the investigations are left to the PPD and freelance heroes (some of which actually work for Freedom Corps, though most are their own bosses), and Freedom Corps sends in their troops if it's determined they are sorely needed (which is hardly ever the case, thanks to the involvement of our heroes).
At the moment, I figure Freedom Corps acts as an information gathering agency/military force for situations that have a more immediate impact. They probably track the movements of particular heroes, villains and unaffiliated meta humans to determine whether or not situations are about to erupt into world-threatening problems. This is why they have a presence in Atlas Park and Galaxy City(to be constantly checking the new blood), Faultline (potentially world-impacting) the warzones (massive amounts of power coming into conflict in Bloody Bay, Siren's Call, Warburg and Recluse's Victory) and the Rikti Warzone (self-explanatory), but you don't see them patrolling everywhere.
My Stories
Look at that. A full-grown woman pulling off pigtails. Her crazy is off the charts.
I sincerely apologize if I should be asking this in some other forum, but I figure since my question is RP based, this seems like the right place. I have this idea for a story that's been bouncing around in my head for the better part of a week. I started to flesh out some more specifics on it today, but I need some Longbow information that I couldn't find on the official site or ParagonWiki.
My question is, what is the scope of Longbow's authority? I know they're a military arm of Freedom Corps, and that they're supplied by and partially funded by NATO, but how much authority do they have? We now have packs of Longbow Eagles patrolling the streets of Paragon City, and LB routinely responds to acts of meta-villain mayhem within the city. But these seem to be largely reactive actions (I know the situation in the RI is different). Does Longbow authority, within Paragon City, extend beyond the PPD? Does Longbow conduct investigations and make arrests involving meta-humans other than the arrests made during a response to a crime in progress?