why would native americans be interested in the outcome of the american revolution?

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"Initially both sides in the war urged the Native Americans to stay out of the conflict. But by 1776 both sides courted the Iroquois Confederacy. Brant succeeded in getting 4 of the 6 Iroquois tribes (Mohawks, Cayugas, Onondagas, and Senecas) to fight for the British, and warriors from the other two tribes, the Oneidas and Tuscaroras, fought with the Americans. This forever dissolved the Confederacy which had kept the tribes a strong force in the north. Other Native tribes in the south also took sides.

Most fought with the British, but all lost in the Peace which followed. The Preliminary Articles of Peace of 1782 did not mention the Native Americans at all. Brant was outraged that the British were selling out the tribes.The British failed to set aside areas which were promised by Treaties they had made with the tribes.

The British views were mixed. "It might have been easily reserved and inserted that those lands the Crown relinquished to all the Indn. Nations as their Right and property were out of its power to treat for, which would have saved the Honor of Government with respect to that Treaty," Daniel Claus, the British agent for the Six Nations in Canada write concerning the boundaries of the Indian country established by the Fort Stanwix treaty line of 1768. "Our treaties with them were solemn," Lord Walsingham stated, "and ought to have been binding on our honour." Lord Shelburne, on the other hand, defended the Preliminary Articles, asserting that "in the present treaty with America, the Indian nations were not abandoned to their enemies; they were remitted to the care of neighbours."

In 1783, under the terms of the Peace of Paris, without regard to its Indian allies, Britain handed over to the new United States all its territory east of the Mississippi, south of the Great Lakes, and north of Florida even though much of that land was not British according to its treaties with native tribes."

Source:

http://www.historywiz.com/nativesrevolution.html