Does anybody know any example of a semistable and nonsimple sheaf on a K3 surface $S$?
The trival sheaf $\mathcal O_S\oplus\mathcal O_S$ is one: it has nontrivial global endomorphism algebra $gl_2(k)$ and is semistable. 


Does anybody know any example of a semistable and nonsimple sheaf on a K3 surface $S$? 


The trival sheaf $\mathcal O_S\oplus\mathcal O_S$ is one: it has nontrivial global endomorphism algebra $gl_2(k)$ and is semistable. 

