  We find a full strongly exceptional collection for the Cayley plane OP2, the
simplest rational homogeneous space of the exceptional group E6. This
collection, closely related to the one given by the second author in [J.
Algebra, 330:177-187, 2011], consists of 27 vector bundles which are
homogeneous for the group E6, and is a Lefschetz collection with respect to the
minimal equivariant embedding of OP2.
