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.
If the lulav was taken without permission, knowing thàt the owner does not want to lend it, the Shulchan Aruch Orach Chaim 649:1 applies:
.כל ארבעה המינים פסולים בגזול ובגנוב
All 4 speicies one has not fullfiled ones obligation if it is stolen
Even when borrowed with permission e.g the owner always let's that person use his things, on the first day one has not fulfilled ones obligation as stated ibid 649,2 :
וכן שאול ביום ראשון משום דבעינן לכם:
A borrowed lulav is also invalid
Therefore she cannot make a Brocho in this case rather she has to own the lulav via the owner giving it to her as a present which she can then return. (On the other days except the first she can borrow the lulav as long as she knows the owner let's her and she can make a brocho.)
