I think this is a very interesting question. Certainly, the name of the language ties it to its home country, England, but even there it never was a truly native language. Around 450 AD, a number of Germanic tribes (primarily the Angles, Saxons, and Jutes) invaded what is now England and brought with them the Germanic language that would become known as English. Before that invasion, people were speaking languages from prior invasions, including Latin and Celtic.
Even the history of the language, then, complicates the idea that any one country or group of people owns it. (lorijayne's comments seem to me right on the mark!) Today you'll even hear a number of language scholars talking about World Englishes, which suggests that there's no longer one language that can be owned by any one group of people.
In your question you mention "the role and nature of English," which seems to suggest to me that you, too, understand how English has become a global language and has undergone any number of transformations in the process.
Language is connected to people, not to a nation-state. In this way, language is the property of whichever country chooses to use it. While English originated in England, as a consequence of disseminating it through empire, it no longer belongs to England alone. Further, many of England's former colonies have replaced her in power and prestige.
Secondly, languages evolve within a local setting. While American English has spread globally, it is seen as foreign outside of the United States. In India, English is a common language and it's evolution is different that in places where it is the primary languages. However, Indian English is no less valid a language than any other forms of English.
in short, English belongs to any country that chooses to use it.