  In this paper we show that if a cosimplicial space or spectrum $X^\bullet$
has a certain kind of combinatorial structure (we call it a $\Xi^n$-structure)
then the total space of $X^\b$ has an action of a certain operad which is
weakly equivalent to the little n-cubes operad. The $n\leq 2$ case was proved
by a more complicated argument in our earlier paper A Solution of Deligne's
Hochschild Cohomology Conjecture
(http://front.math.ucdavis.edu/math.QA/9910126). In the special case
$n=\infty$, we define a symmetric monoidal structure $\boxtimes$ on
cosimplicial spaces and show that if $X^\b$ is a commutative $\boxtimes$-monoid
then the total space of $\X^\b$ is an $E_\infty$ space.
