Being British, my knowledge of Native American history is very limited, so I can't comment on the accuracy of the film, but being Hollywood, I would trust the authenticity about as much as the move "Braveheart". What I can say is that I found it a gripping and tragic story, well acted with good direction. Very few US westerns show the mistreatment of Native Americans, it makes a change.
Review of Cheyenne Autumn
