In 1066, the count of Yaroslavl has a stroke of genius, leading to his building a dynasty that spans the centuries, unifying Russia and Scandinavia under one flag.
As the centuries move onward from 1419 to 1819, the Swedish Empire discovers the New World and colonizes all of real world present-day Canada and the United States, running it as a fiefdom. Sweden becomes one of the world's two major superpowers along with China.
The 19th century sees the Swedish Empire rapidly industrialize and add population while the US and Canada are given their independence peacefully, puppets of the mother country. The center of mass of industrial power lies in Eastern Europe, as present-day Estonia becomes the locus of the entire world financial and industrial community. China continues to dominate Asia as the two superpowers divide the world according to their whim.
However, this balance of power must eventually lead to conflict, and in 1936 the Great War breaks out. Sweden crushes the Chinese, subsuming their industry and people and finally completing the conquest of the world in 1953. All hail Sweden!
(this was a rough abstract of exactly what happened in a Paradox four-game spanning save...my most successful Paradox 900.)