If a person takes something belonging to someone else under a strong assumption that the owner would permit it, and only after formally requested permission to take the said item were they עבר? If yes, must they ask forgiveness for taking that which they knew would be (and later was expressly) permitted to them?
Taking something assuming he will permit, but does not actually permit is a matter of dispute. The opinion of the SHach [C:M 358:1] is to permit, while the SHulchan Aruch Harav [hichos metziah 4] forbids.
However if it is something which people are commonly free to lend out, it would seem is permissible according to all opinions. [Pischei CHoshen Gneiva chapter 1 halacha 15].