  In this paper we introduce a group invariant version of the wellknown Ekeland
variational principle. To achieve this, we defne the concept of convexity with
respect to a group and establish a version of the theorem within this
framework. Additionally, we present several consequences of the group invariant
Ekeland variational principle, including Palais-Smale minimizing sequences, the
Br{\o}nsted-Rockafellar theorem, and a characterization of the linear and
continuous group invariant functionals space. Moreover, we provide an
alternative proof of the Bishop-Phelps theorem and proofs for the
group-invariant Hahn-Banach separating theorems. Finally, we discuss some
implications and applications of these results.
