  We study anti-holomorphic involutions of the moduli space of principal
$G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a complex
semisimple Lie group. These involutions are defined by fixing anti-holomorphic
involutions on both $X$ and $G$. We analyze the fixed point locus in the moduli
space and their relation with representations of the orbifold fundamental group
of $X$ equipped with the anti-holomorphic involution. We also study the
relation with branes. This generalizes work by
Biswas--Garc\'{\i}a-Prada--Hurtubise and Baraglia--Schaposnik.
