The Kingdom of Grand Inca was a kingdom formed out of the Vice-Royalty of Grand Inca, a Byzantine Colony in the South American continent, during the uprisings that resulted in the Grand Byzantine Republic in 1851. Centred around the old Inca city of Lima, the Kingdom dominated South America for the latter half of the 19th century, succumbing only in 1903 to nationalist rebellions by minorities such as the Chileans and Neo-Mayans, who formed a collection of separate states.
To begin with, the independence of the kingdom could hardly be attributed to the Incas at all; if neither the Byzantines had had a civil war, nor the Confederate States of North America claimed their independence, then the independence movement of the Inca's would never have been achieved. Without very much action of their own, the Incas saw their former provincial leaders flee in droves before them. It was fairly easy after that; a nationalist Inca army marched on the Byzantine Viceroy's residents in Novio Piraeus, and put it to the sack. About 100 miles down the coast, in the small town of Lima, King Faro I was proclaimed by a native assembly.
War with the Grand Byzantine Republic
If the Incas hadn't done anything to gain their independence, they maintained it tenaciously - annihilating the isolated Byzantine forts dotted along the Andes and establishing firm hold on an area embracing land from the forests of Ecuador and Venezuela to the southern tip of the continent.