Hello! You asked what the shawl symbolizes in the novel Fasting, Feasting. In a nutshell, the shawl symbolizes control.
With the favored son of Mama and Papa in the United States for his college studies, Uma is tasked with putting together a care package for her brother, Arun. She includes what her parents tell her to put in; among other things, she puts in a box of Indian tea and a shawl Mama has bought at the Kashmir Emporium. Toward the end of the novel, we find that Arun has given his box of tea and his Indian shawl to Mrs. Patton as a gift. For the first time in his life, Arun finds himself free of any form of coercion; he wants to decide who he is, where he is going in life, and what he will do with his life. To that end, he does not want to be entangled in any relationship (whether with his countrymen in exile or any American he meets); this is why he gives away his shawl and why he decides not to stay with Mrs. O'Henry's sister during the summer break. It is symbolic of his desire to decide his destiny.
It was the first time in his life away from home, away from MamaPapa, his sisters, the neighbourhood of old bungalows, dusty gardens and straggling hedges where he had grown up, the only town he had ever known; he had at last experienced the total freedom of anonymity, the total absence of relations, of demands, needs, requests, ties, responsibilities, commitments.
He was Arun. He had no past, no family and no country.
The summer in the US stretched out open, clear and blank. Arun had every intention of keeping it so.
Thanks for the question.