  The derived category of a general complete intersection of four quadrics in
P^{2n-1} has a semi-orthogonal decomposition < O(-2n+9), ..., O(-1), O, D >,
where D is the derived category of twisted sheaves on a certain non-algebraic
complex 3-fold coming from a moduli problem. In particular, when n=4 we obtain
a (twisted) derived equivalence of Calabi-Yau 3-folds predicted by Gross. This
differs from Kuznetsov's result in that our construction is geometric and
avoids non-commutative varieties.
