  We give a unified generalization of Dugas' construction on stable
auto-equivalences of Morita type from local symmetric algebras to arbitrary
symmetric algebras. For group algebras $kP$ of $p$-groups in characteristic
$p$, we recover all the stable auto-equivalences corresponding to endo-trivial
modules over $kP$ except that $P$ is generalized quaternion of order $2^m$.
Moreover, we give many examples of stable auto-equivalences of Morita type for
non-local symmetric algebras.
