  We construct a full exceptional Lefschetz collection on the spinor 15-fold
consisting of a connected component of the space of orthogonal 6-dimensional
subspaces of a 12-dimensional complex vector space, isotropic with respect of a
fixed non-degenerate quadratic form. The collection is made of 2 twists of a
4-item block and 8 twists of a 3-item block, confirming a conjecture of
Kuznetsov and Smirnov. We speculate that a similar collection might work for
the Freudenthal E7-variety.
