The NWMP went west (The Great March) in 1873 to quell the Indian problem. In 1870 the Dominion of Canada acquired sovereignty over what would become the provinces of Manitoba, Saskatchewan and Alberta.
"In the minds of most eastern Canadians the territory was perceived as a lawless frontier where drunken and savage Indians murdered and scalped settlers. Their suspicions were confirmed by a British Officer, Lt. William Butler, who was commissioned by the government to survey the country in 1871. Butler dubbed it "The Great Lone Land" and reported that "The institutions of Law and Order, as understood in civilized communities, are wholly unknown."
"Sir John A. Macdonald's answer to the problem of disorder and the threat of Indian violence in the North-West Territories was to organize a force of "Mounted Riflemen, trained to act as cavalry, but also instructed in the Rifle exercise." This body, Canada's first Prime Minister conceived, "should not be expressly Military but should be styled Police, and have the military bearing of the Irish Constabulary".
"It would proceed to the western plains, establish law and order and reach a peaceful understanding with the Indian nations about their future and that of their traditional hunting grounds in advance of settlement. In this manner Canada would avoid the armed conflict associated with expansion on the American frontier, the prairies would be peacefully opened up to white settlers and the railway could be built that would link Canada with British Columbia."
Recruiting for the 300-man force began in the fall of 1873. The following year, under command of Commissioner George A. French, the NWMP made it's epic march from Manitoba to the foothills of the Rocky Mountains. They put an end to the whisky trade that was decimating the Indians and the wolfers that were poisoning other game, but with the decline of the buffalo herds and the increase of settlement, relations with the NWMP deteriorated rapidly.
In 1876, after the Custer debacle, Sitting Bull was allowed into Canada with his Sioux as long as they didn't stir up trouble with Canadian Indians. Eventually they were returned to the US to face US justice. Relations between the RCMP and the Indians haven't improved much since.
Sorry for the rant. It's a rainy day and I'm bored out of my skull. Spent most of it cleaning guns.
The difference between the U.S. old west and the Canadian old west is that in the U.S. the settlers went west first, then came law enforcement, such as it was at the time. In Canada the law (North West Mounted Police) went west first, established law and order, had the Indian treaties signed, and then the settlers came.