  The purpose of this article is to show a version of d\'evissage theorem of
non-connective $K$-theory. Our theorem contains Quillen's d\'evissage theorem,
Waldhausen's cell filtration theorem and theorem of heart as special cases. In
this sense, we give an affirmative answer to Thomason's problem in
Thomason-Trobaugh's paper. We introduce the notions of cell structures and
d\'evissage spaces and our main theorem states a structure of non-connective
$K$-theory of d\'evissage spaces in terms of non-connective $K$-theory of heart
of cell structures. A specific feature in our proof is 'motivic' in the sense
that properties of $K$-theory which we will utilze to prove the theorem are
only categorical homotopy invariance, localization and co-continuity. On the
other hands, it is well-known that the analogue of the d\'evissage theorem for
$K$-theory does not hold for Hochschild homology theory. In this point of view,
we could say that d\'evissage theorem is not 'motivic' over dg-categories. To
overcome this dilemma, the notion of d\'evissage spaces should not be expressed
by the language of dg-categories. First three sections are devoted to the
foundation of our model of stable $(\infty,1)$-categories which we will play on
to give a description of d\'evissage spaces.
