  Let X be an algebraic variety with an action of an algebraic group G. Suppose
X has a full exceptional collection of sheaves, and these sheaves are invariant
under the action of the group. We construct a semiorthogonal decomposition of
bounded derived category of G-equivariant coherent sheaves on X into
components, equivalent to derived categories of twisted representations of the
group. If the group is finite or reductive over the algebraically closed field
of zero characteristic, this gives a full exceptional collection in the derived
equivariant category. We apply our results to particular varieties such as
projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.
