  We translate the concept of the join of topological spaces to the language of
$C^*$-algebras, replace the $C^*$-algebra of functions on the interval $[0,1]$
with evaluation maps at $0$ and $1$ by a unital $C^*$-algebra $C$ with
appropriate two surjections, and introduce the notion of the fusion of unital
$C^*$-algebras. An appropriate modification of this construction yields the
fusion comodule algebra of a comodule algebra $P$ with the coacting Hopf
algebra $H$. We prove that, if the comodule algebra $P$ is principal, then so
is the fusion comodule algebra. When $C=C([0,1])$ and the two surjections are
evaluation maps at $0$ and $1$, this result is a noncommutative-algebraic
incarnation of the fact that, for a compact Hausdorff principal $G$-bundle $X$,
the diagonal action of $G$ on the join $X*G$ is free.
