  We define and discuss some general properties of residual categories of
Lefschetz decompositions in triangulated categories. In the case of the derived
category of coherent sheaves on the Grassmannian $\text{G}(k,n)$ we conjecture
that the residual category associated with Fonarev's Lefschetz exceptional
collection is generated by a completely orthogonal exceptional collection. We
prove this conjecture for $k = p$, a prime number, modulo completeness of
Fonarev's collection (and for $p = 3$ we check this completeness).
