The phrase "advanced a theory" is correct and usable in written English.
You can use this phrase when referring to someone who has proposed an idea or solution, usually in a scholarly context. For example, "Albert Einstein advanced a theory of relativity which revolutionized our understanding of the universe."
Mr. Donovan advanced a theory of pop evolution.
He also advanced a theory of chemical indicators.
He advanced a theory of economic development that contained several elements that brought him largely posthumous fame.
In the late 1940s he advanced a theory of the formation of the Earth from a rotating cloud of dust and gas.
In 1963 Berkner, with L.C. Marshall, advanced a theory to describe the way in which the atmospheres of the solar system's inner planets had evolved.
Pressure to admit the ruse has been building on Ms. Albert since October, when New York magazine published an article that advanced a theory that she was the author of JT Leroy's books.
Bieberbach was an enthusiastic proponent of Nazi ideology, publicly advancing a theory of racial and national differences in mathematical style.
There are so many unanswered questions in ancient history, questions that the novelist, where the historian may tremble to advance a theory, may joyfully answer with invention.
Long before September 11th, but with increasing stridency since then, he has been advancing a theory about the "pivotal" role that Britain can play in world affairs.
Rather than advancing a theory of his own, he compares all the available theories, consults the experts -- self-appointed or otherwise -- and weighs their judgments one against the other, attempts to steer a sensibly skeptical middle course.
It was built, in 1975, by the Polynesian Voyaging Society, a group of Hawaiians eager to revive awareness of their indigenous culture and to advance a theory of how humans settled the islands of the Pacific.
