  For $\mathbb{G}$ an algebraic (or more generally, a bornological) quantum
group and $\mathbb{B}$ a closed quantum subgroup of $\mathbb{G}$, we build in
this paper an induction module by explicitly defining an inner product which
takes its value in the convolution algebra of $\mathbb{B}$, as in the original
approach of Rieffel \cite{Rieffel}. In this context, we study the link with the
induction functor defined by Vaes. In the last part we illustrate our result
with parabolic induction of complex semi-simple quantum groups with the
approach suggested by Clare \cite{Clare}\cite{CCH}.
