Analytic atlases on
can be easily defined making it an
n-dimensional complex manifold. Then with the help of bi-M
öbius transformations in complex coordinates Abelian groups are constructed making this manifold a Lie group. Actions of Lie groups on differentiable manifolds are well known and serve different purposes. We have introduced in previous works actions of Lie groups on non orientable Klein surfaces. The purpose of this work is to extend those studies to non orientable
n-dimensional complex manifolds. Such manifolds are obtained by factorizing
with the two elements group of a fixed point free antianalytic involution of
. Involutions
h(z) of this kind are obtained linearly by composing special M
öbius transformations of the planes with the mapping
. A convenient partition of
is performed which helps defining an internal operation on
and finally actions of the previously defined Lie groups on the non orientable manifold
are displayed.