Isn’t most of Oklahoma Indian Reservations? They probably have a lot to do with that.
Actually no, not really at all, not in the usual, traditional terms of "Indian Reservations".
There IS a 9th grade Oklahoma public school history lesson here, which I'll spare you, but to your question:
SOME of the highways in Oklahoma ARE under the jurisdiction of some of the tribes, but honestly I couldn't tell you where any of the interstate highways are. So far as I know, the Interstate highways, which includes all the toll highways, are under OHP's jurisdiction.
Just hypothetically, drive from DFW north on I-35 to the Kansas border, and you won't be under the legal jurisdiction of any of the tribes unless you stop at a casino and get in trouble.
(Just to make things a bit more complicated, because of a recent SCOTUS ruling, any Oklahoman ANYWHERE who is a member of a tribe, and commits a crime - is headed to tribal court. Which according to some I've talked to, is worse than going to "regular" district court. The tribes don't like criminals either - which may have something to do with your original question. But I don't believe this applies for traffic tickets. We're talking misdemeanors and felonies here.)
With the OHP on the job, driving faster than the mainstream of the traffic is a good way to get a polite speeding ticket. So I've been told...
Oh yeah this is also true on the "Indian highway" that runs from the Cimarron Turnpike north to Ponca City. The tribal police are in charge of some of that particular state highway, and they have radar guns too...