Outer derivations on blocks of group algebras

Let $B$ be a block of a finite group algebra $kG$. Linckelmann has conjectured that if the defect group $P$ of $B$ is nontrivial then $B$ admits a $k$-linear outer derivation, or in other words $\operatorname{HH}^1(B)\neq 0$. We provide various criteria for the non-vanishing of $\operatorname{HH}^