The Grand Theft Auto games were invented by a Scotsman called "David Jones", he made the games in Scotland (North Britain) with his game company "DMA Designs" which he founded in 1988 - which was based in Dundee, Scotland.
Then two English brothers "Sam & Dan Houser" took the company and the GTA Franchise (from GTA III onwards) they then opened up a main publishing office in New York and called it "Rockstar Games". They then changed game company "DMA Designs" in Britain to "Rockstar North" and this is where all the GTA games are developed (apart from the portable versions which are handled from "Rockstar Leeds" in England/ South Britain)
The game engine that powerd GTA III,Vice City,San Andreas and portable versions "Renderware" was created by English games company Criterion Games (the makers of the Burnout franchise)
Rockstar Games has many sub divisions all over the world which handle the publishing and localisation in their respective countries, but most of them are in Britain, Rockstar North (all main GTA games are made here) Rockstar Leeds, in England (all portable GTA games are handled from here) Rockstar London & Rockstar Lincoln.
"David Jones" the inventor of the GTA franchise went on to invent the "Crackdown" franchise for Microsoft, he also created many other classic games like the well known "Lemmings" franchise.