  We investigate Hochschild cohomology and homology of admissible subcategories
of derived categories of coherent sheaves on smooth projective varieties. We
show that the Hochschild cohomology of an admissible subcategory is isomorphic
to the derived endomorphisms of the kernel giving the corresponding projection
functor, and the Hochschild homology is isomorphic to derived morphisms from
this kernel to its convolution with the kernel of the Serre functor. We
investigate some basic properties of Hochschild homology and cohomology of
admissible subcategories. In particular, we check that the Hochschild homology
is additive with respect to semiorthogonal decompositions and construct some
long exact sequences relating the Hochschild cohomology of a category and its
semiorthogonal components. We also compute Hochschild homology and cohomology
of some interesting admissible subcategories, in particular of the nontrivial
components of derived categories of some Fano threefolds and of the nontrivial
components of the derived categories of conic bundles.
