  S-folds are a non-perturbative generalization of orientifold 3-planes which
figure prominently in the construction of 4D $\mathcal{N} = 3$ SCFTs and have
also recently been used to realize examples of 4D $\mathcal{N} = 2$ SCFTs. In
this paper we develop a general procedure for reading off the flavor symmetry
experienced by D3-branes probing 7-branes in the presence of an S-fold. We
develop an S-fold generalization of orientifold projection which applies to
non-perturbative string junctions. This procedure leads to a different 4D
flavor symmetry algebra depending on whether the S-fold supports discrete
torsion. We also show that this same procedure allows us to read off admissible
representations of the flavor symmetry in the associated 4D $\mathcal{N} = 2$
SCFTs. Furthermore this provides a prescription for how to define F-theory in
the presence of S-folds with discrete torsion.
