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We show that Sarnak's conjecture on M\"obius disjointness holds in everyuniquely ergodic modelof a quasi-discrete spectrum automorphism. A consequenceof this result is that, for each non constant polynomial $P\in\R[x]$ withirrational leading coefficient and for each multiplicative function$\bnu:\N\to\C$, $|\bnu|\leq1$, we have\[ \frac{1}{M} \sum\_{M\lem\textless{}2M} \frac{1}{H} \left| \sum\_{m\le n \textless{} m+H} e^{2\piiP(n)}\bnu(n) \right|\longrightarrow 0 \] as $M\to\infty$, $H\to\infty$,$H/M\to 0$.

Automorphisms with quasi-discrete spectrum, multiplicative functions and average orthogonality along short intervals