This paper is a continuation of the papers Moduli spaces
of decomposable morphims of sheaves and quotients by non-reductive groups
and Espace abstraits de morphismes et mutations. I show here that
the method used in the first paper to construct moduli spaces of morphisms
and the one used in the second paper to extend the results of the first
are particular cases of a more general method of construction of algebraic
quotients. It is based on the notion of quasi-isomorphism. Let G,
algebraic groups acting on algebraic varieties X, X' respectively.
A quasi-morphism is a map
that can be everywhere locally lifted to morphisms from open subsets of
to X' (plus some additional technical conditions...). A
is a quasi-morphism which is bijective and whose inverse is also a quasi-morphism.
If there is a quasi-isomorphism between X and X'it is possible
to deduce the existence of algebraic quotients of open subsets of X
from the existence of quotients of the corresponding open subsets
X'. The method used to construct moduli spaces of morphisms is
extended in this paper to complexes of decomposables sheaves.