  We develop here a concept of deformed algebras and their related groups
through two examples. Deformed algebras are obtained from a fixed algebra by
deformation along a family of indexes, through formal series. We show how the
example of deformed algebra used in \cite{Ma2013} is only an example among
others, and how they often give rise to regular Fr\"olicher Lie groups, and
sometimes to Fr\'echet Lie groups, that are regular. The first example, indexed
by $\mathbb{N},$ is obtained by deformations of the group of bounded classical
pseudo-differential operators $Cl^{0,*}$ by algebras of (maybe unbounded)
classical pseudo-differential operators. In the second one, the set of indexes
is a $\N-$graded groupo\"id, which is made of manifolds with boundary that are
understood as morphisms of cobordisms. Here again, we get regular Lie groups,
and we show how this setting applies to a class of examples that are derived of
so-called stochastic cosurfaces.
