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The man, identified as Kamil, walked into the Kamla Market police station in north Delhi in the early hours of Sunday and confessed to the murder, they said.
He told police the body was lying inside their second floor flat in Kamla Market area.
Police found the body of 22-year-old Reshma. The body had already turned blue, a senior police officer said, adding that the murder might have taken place on Friday.
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Kamil told police he was drunk and had a quarrel with Reshma on Friday over her friendship with two men, the officer said.
He admitted that he beat her up and strangled her later, he added.
The couple were married for three years and Kamil worked as a peon at the Ambedkar University, police said.