  We present a geometric proof of Bernstein's second adjointness for a
reductive $p$-adic group. Our approach is based on geometry of the wonderful
compactification and related varieties. Considering asymptotic behavior of a
function on the group in a neighborhood of a boundary stratum of the
compactification, we get a "co-specialization" map between spaces of functions
on various varieties with $G\times G$ action. These maps can be viewed as maps
of bimodules for the Hecke algebra, and the corresponding natural
transformations of functors lead to the second adjointness. We also get a
formula for the "co-specialization" map expressing it as a composition of the
orishperic transform and inverse intertwining operator; a parallel result for
$D$-modules was obtained in arXiv:0902.1493.
  As a byproduct we obtain a formula for the Plancherel functional restricted
to a certain commutative subalgebra in the Hecke algebra, generalizing a result
by Opdam.
