We study stable homomorphisms for twisted bimodule structures on a finite-d
imensional self-injective algebra. We use this to give a presentation for t
he Hochschild cohomology ring of self-injective Nakayama algebras. By deriv
ed equivalence, this gives also the Hochschild cohomology ring for arbitrar
y self-injective whose stable Auslander-Reiten quiver is of the form ZA(n)/
[tau(e]). Moreover, we obtain a new characterization of self-injective Naka
yama algebras.