  We show that the Poincar\'e bundle gives a fully faithful embedding from the
derived category of a curve of sufficiently high genus into the derived
category of its moduli space of bundles of rank $r$ with fixed determinant of
degree 1. Moreover we show that a twist of the embedding, together with 2
exceptional line bundles, gives the start of a semi-orthogonal decomposition.
This generalises results of Narasimhan and Fonarev-Kuznetsov, who embedded the
derived category of a single copy of the curve, for rank 2.
