The irony of education
Instead of being a virtuous thing, Archilde's education works against him in his community because his time away has led him to develop differently than the other people in his community, and the desperate reality of the situation on the reservation make the community more likely to reject foreign influences. So ironically, he suffers for his enlightenment.
"Rejected by his homeland”
To say someone is rejected by their homeland is to say that they might be prophetic, according to the ancient Jewish belief that a true prophet will be rejected by his home lands. By showing this happen to Archilde, the reader is asked to consider Archilde as a significant religious figure—a martyr of his community. But for Archilde, it's tragic and ironic the entire time.
The wrongful arrest
The community scapegoats Archilde by framing him for two murders. He ends up being arrested for a situation he had nothing to do with, and the implication is that things will not go well for Archilde.
The mother's sin atoned
Archilde's mother was the real murderer in one of the two murders. Ironically, Archilde's arrest means that his own mother will get away with murder, as if he laid his life down to take her place, but in this case, it happened involuntarily.
The irony of religion
There is no sense that anyone in the community has a sustainable religious life. The father is left with his own fading tradition. The mother has her fading Indian tradition, and although she tries to revive her religious life, there's a sense in which that pursuit is strained and anxious. The only 'religious' authority in the novel is Archilde himself, not because of his dogmatic obedience to one way of life, but because of his open-mindedness and his education.
