In the story “The Red Convertible,” what contrasts does the story draw between the world of the reservation and the white American society beyond? What does it have to say about the way Native Americans are treated? How does it ultimately embrace and celebrate Native American values?

Louise Erdrich's "The Red Convertible" revolves around the relationship of two brothers—Lyman and Henry—who live on a Native American reservation. The titular car is a symbol of their relationship as well as their sense of adventure and desire to experience life outside of the reservation. Ironically, it is Henry's time away at war that changes him and his relationship with his brother forever.
Early in the story, the narrator, Lyman, recalls when he and Henry got the convertible. Lyman begins the story by saying,

I was the first one to drive a convertible on my reservation. And of course it was red, a red Olds. I owned that car along with my brother Henry Junior.

This already tells the reader that the brothers's fascination with the car is more representative of life outside of the reservation ("American life") than on it. The brothers obtain the car and take it on a great adventure that becomes the source of Lyman's nostalgia and sets up the contrast between Henry's character before and after the war. Lyman notes that he was able to earn money and says that is unusual for a Chippewa, again highlighting a difference between Native American life and the life of Americans off the reservation. This money helps the brothers buy the convertible. Lyman says, "We took off driving all one summer," and he recaps the great times they had, the girls they met, and the places they saw. The world outside the reservation is presented as one of possibility and leisure.
Later, Henry joins the army and serves in Vietnam. Lyman writes,

It was at least three years before Henry came home. By then I guess the whole war was solved in the government's mind, but for him it would keep on going.

Henry suffers sever PTSD from his experiences in Vietnam and is clearly depressed when he returns to the reservation. In this case, his time away from home stands in stark contrast to the previous car trip he and his brother enjoyed. At one point, Lyman discusses the issue of treatment for Henry, and the conversation involves medicine on the reservation and off. He notes that there are "no Indian doctors on the reservation," and the boys's mom doesn't trust the reservation's medicine man because he previously tried to romance her. Lyman and his mom decide that vet hospitals, even if they could get him there, would not help Henry. The only solution Lyman can come up with is to have Henry work on the car (even though it's in perfect shape) as a way to deal with his trauma. Henry does, indeed, throw himself into work on the car, but it ultimately does not "heal" or save him. He ends up committing suicide by drowning himself in the river and Lyman sends the car in after him, as their relationship, symbolized by the car, is effectively over.
It is both ironic and tragic that Henry and the convertible end up here. The car represented so much potential for adventure and for worlds outside of the reservation, but ultimately, it is his time off the reservation in the war, fighting for the country that marginalized him, that led to Henry's demise.