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Let $X$ be a K3 surface which doubly covers an Enriques surface $S$. If$n\in\mathbb{N}$ is an odd number, then the Hilbert scheme of $n$-points$X^{[n]}$ admits a natural quotient $S_{[n]}$. This quotient is an Enriquesmanifold in the sense of Oguiso and Schr\"oer. In this paper we construct slopestable sheaves on $S_{[n]}$ and study some of their properties.

Descent of tautological sheaves from Hilbert schemes to Enriques manifolds