  Twisting process for quantum linear spaces is defined. It consists in a
particular kind of globally defined deformations on finitely generated
algebras. Given a quantum space (A_1,A), a multiplicative cosimplicial
quasicomplex C[A_1] in the category Grp is associated to A_1, in such a way
that for every n a subclass of linear automorphisms of A^{\otimes n} is
obtained from the groups C^n[A_1]. Among the elements of this subclass, the
counital 2-cocycles are those which define the twist transformations. In these
terms, the twisted internal coHom objects, constructed in a previous paper (cf.
math.QA/0112233), can be described as twisting of the proper coHom objects,
enabling us in turn to generalize the mentioned construction. The
quasicomplexes C[V], V a vector space, are studied in detail, showing for
instance that, when V is a coalgebra, the quasicomplexes related to Drinfeld
twisting, corresponding to bialgebras generated by V, are subobjects of C[V].
