One the facebook page you can follow the timeline. Literally in November of 2011 some of their "research" showed Dragging Canoe's ancestors to be Powhatan, Tuscarora and Shawnee....
https://www.facebook.com/pages/RedNation-Chickamauga/128946590500045"Through the years things get lost or turned around. I and others have been researching and now have documented proof on this; Moytoy (Grandfather of Dragging Canoe) was Powhatan; Attakullakulla (Little Carpenter) (Father of Dragging Canoe) was taken in a raid in Canada by the Cherokee as a baby and he was Nipissing. He later married a woman named Nionee (Mother of Dragging Canoe) who was Tuscarora and Shawnee. Together they had a son Named Dragging Canoe who became the leader of the Chickamauga. From all this it makes the Chickamauga Indians a branch of the Anishinabe / Algonquin."
Before that post they were clearly still calling themselves Cherokee. The premise of the "tribe" is that they are all descendents of Dragging Canoe, who they now say was not Cherokee (except they didn't know that till recently....whoops).
Some of the comments have people asking "ok what about Cherokees?" with no response.....seems they don't know what they are now.....
The timeline still includes all the previous posts of the Red Nation of the Cherokee: Chickamauga Band (which is the previous iteration of this group, now going by Red Nation Chickamauga Band. They are definitely selling themselves as Algonquin/Anishnabe now.....
In reading some of the pages of the group members, there has literally been a change with some from greeting each other with "O'siyo" to now saying "Boozhoo"....
Superdog