Here's some of the crucial bits form another page re' jurisdiction:

Under the Major Crimes Act, the federal government has jurisdiction over major crimes committed on Indian reservations, and these crimes are violations of federal law. Public Law 280, passed by Congress in 1953, allows the states to choose to share responsibility with the federal government for investigating and prosecuting a variety of criminal cases. Tribal police forces, which have the greatest interest in maintaining law and order on their reservations, have very limited authority, as a result of recent United States Supreme Court decisions.

In Oliphant v. Suquamish Indian Tribe, the Supreme Court held that tribes do not have criminal jurisdiction over non-Indians. In Duro v. Reina, decided this year, the Court extended this principle to anyone who was not a member of the tribe. In both cases the Court reasoned that because Indian tribes have only limited sovereignty, they cannot prosecute an outsider unless Congress delegates this authority, and the Court concluded that Congress had not done so. According to Michael Hawkins, a former U.S. Attorney for Arizona, the precedent set by the Supreme Court's decision in Oliphant "is a significant impediment to maintaining law and order and safe