Multiplicative Higgs bundles and involutions

In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a multiplicative Higgs bundle taking values in a symmetric variety associated to $\theta$, or in an equivariant embedding of it. We also study how these objects appear as fixed points of involutions of the moduli space of multiplicative $G$-Higgs bundles, induced by the involution $\theta$.