Let $\Lambda$ be a finite-dimensional self-injective algebra (over an algebraically closed field, if necessary). Let $Pic(\Lambda)$ be the group of natural isomorphism classes of self-equivalences $mod(\Lambda)\rightarrow mod(\Lambda)$ of the category $mod(\Lambda)$ of finite-dimensional right $\Lambda$-modules. Similarly, let $StPic(\Lambda)$ be the group of natural isomorphism classes of self-equivalences $\underline{mod}(\Lambda)\rightarrow \underline{mod}(\Lambda)$ of the stable category $\underline{mod}(\Lambda)$ of finite-dimensional right $\Lambda$-modules. What can we say about the kernel of the obvious morphism $Pic(\Lambda)\rightarrow StPic(\Lambda)$? Is there any known example of non-trivial element in the kernel? I'm particularly interested in the case of $\Lambda$ being of finite representation type.