What gender roles does Chaucer satirize in the Wife’s characterization?
Satire involves an author taking a serious tone toward a subject, but then exaggerating some element until it's clear that the real purpose is to make fun of some aspect of society. Chaucer's work is complex, and the Wife of Bath satirizes a number of gender roles throughout her prologue and tale, so there's no one answer to this.
I would start by looking at the prologue. In that, the Wife of Bath creates a complex argument for why women should use their sexuality as a weapon against their husbands. In doing so, she turns conventional wisdom of the time--that men have the power--on its head. At this time in history, a woman was seen as having far less control over herself, which is why she was in need of a male companion to protect her from her own folly. However, the Wife's stories of how women can accuse men of infidelity and keep them on the defensive suggest that women are less victim than predator. This satirizes the traditional view of women as helpless. In fact, after hearing the Wife of Bath speak, the Pardoner talks about his own fear of getting married, which could be seen as making fun of the arrogance of certain men who see themselves as the all-powerful protectors in marriage.
Her fifth marriage to Jenkin nearly goes off the rails when he tries to control the Wife of Bath, reading to her about sinful women and ordering her to stay home. However, the Wife of Bath feigns serious injury after he hits her, and he immediately gives her the power back out of guilt. The story is clearly an exaggeration, and Chaucer appears to make fun of controlling men who think they can keep their wives at home, a common view at the time. It also seems to suggest that the arguments for women being weak and in need of protection are ridiculous. Even though she was much older and physically weaker, the Wife of Bath proved more than a match for Jenkin, and she controlled him.
The gender politics continues in the tale. The knight and even the friars should be symbols of goodness, and yet she describes them as rapists, and makes the knight's sin the center of her tale. Again, the role of men as "protector" takes a fairly large hit here, and that traditional gender role is undermined by the story. And just as in the prologue, the savior is a woman. The traditional role of the woman as second to the man is destroyed when the hag not only has the answer the knight seeks, but she proves a far more effective arguer when they engage. Her defense of poverty leaves the knight unable to refute her points, and unlike some other characters Chaucer creates, the hag does have some valid arguments and solid evidence, making the woman the more logical debater, something which few authors of the time would have even considered.
So Chaucer takes aim at the myth of the female as helpless, ignorant, and pure, and he also aims at the myth of the male as the protector, the dominant partner, and the upholder of moral virtue. Honestly, it's worth going back and rereading the pieces with the gender politics in mind.