  We show that, for each integer n, there exist infinitely many pairs of
n-framed knots representing homeomorphic but non-diffeomorphic (Stein)
4-manifolds, which are the simplest possible exotic 4-manifolds regarding
handlebody structures. To produce these examples, we introduce a new
description of cork twists and utilize satellite maps. As an application, we
produce knots with the same 0-surgery which are not concordant for any
orientations, disproving the Akbulut-Kirby conjecture given in 1978.
