An Ashkenazi woman wants to shake the 4 species on the first day of Sukkot. Her husband doesn't have a lulav. She goes to a friend who has a lulav, and without his knowledge (and active transfer of ownership of the lulav) she takes it to perform the mitzvah. Since she does not co-own the lulav, and there is a requirement that lulav has to belong to the person shaking it on the first day of Sukkot, does she say a bracha on shaking the lulav?
By 'lulav' I refer to all 4 species.