  We construct nontrivial auto-equivalences of stable module categories for
elementary, local symmetric algebras over a field k. These auto-equivalences
are modeled after the spherical twists of Seidel and Thomas and the
$\mathbb{P}^n$-twists of Huybrechts and Thomas, which yield auto-equivalences
of the derived category of coherent sheaves on a variety. For group algebras of
p-groups in characteristic p we recover many of the auto-equivalences
corresponding to endo-trivial modules. We also obtain analogous
auto-equivalences for local algebras of dihedral and semi-dihedral type, which
are not group algebras.
