  We introduce a twisted action of the equivariant cohomology of the singleton
$H_R^\bullet({\rm pt},\Bbbk)$ on the equivarinat cohomology
$H_L^\bullet(X,\Bbbk)$ of an $L$-space $X$. Considering this actions as a right
action, $H_L^\bullet(X,\Bbbk)$ becomes a bimodule togeather with the canonical
left action of $H_L^\bullet({\rm pt},\Bbbk)$. Using this bimodule structure, we
prove an equivariant version of the K\"unneth isomorphism.
  We apply this result to the computation of the equivariant cohomologies of
Bott-Samelson varieties and to a geometric construction of the bimodule
morphisms between these cohomologies.
