The properties of free field theories of arbitrary spin and isospin particles are investigated. Self-conjugate isofermion (I = ½, 32, 52, ⋯) field theories of arbitrary spin S are shown to be nonlocal, with commutators (or anticommutators) failing to vanish outside the light cone. Special attention is given to discrete transformations ℭ, ℑ, and 𝔖. For self-conjugate multiplets the parity, charge conjugation, and time-reversal phase factors ηC, ηP, ηT are not arbitrary but obey ηP2=(−1)2S, ηC2=(−1)2Iηα2, ηT2=(ηα*)2, where the phase ηα = ξ(−1)I+α (|ξ| = 1, α = −I, ⋯, +I) arises when the complex-conjugate representations of SU(2) are transformed to the standard basis. Composite products of ℭ, ℑ, and 𝔖 are discussed, with general phases and attention to the dependence on order of the operators. The six possible ℭℑ𝔖 operations Θi are analyzed. For pair-conjugate multiplets, the operator Θi2 is, in general, a gauge transformation, with phase (ωi*)2 depending on the ℭ, ℑ, 𝔖 phases and the order in which ℭ, ℑ, and 𝔖 enter into Θi. By postulating that Θi2ψΘi−2 be independent of the order of ℭ, ℑ, and 𝔖, we derive the Yang-Tiomno parity factors (±1, ±i) for pair-conjugate fermions. For self-conjugate multiplets, however, the phase restrictions previously stated lead to a unique order-independent result Θ2ψΘ−2=(−1)2I+2Sψ. The usual local field theory result lacks the factor (−1)2I. The latter differs from unity only for the case 2I = odd integer, in which case we are in fact dealing with a nonlocal field theory. The technical details of the theory involve construction of local fields from helicity wavefunctions and helicity particle operators. Fields of spin greater than one are described by the Rarita-Schwinger formalism. An appendix treats in detail the form and properties of the high-spin wavefunctions in the helicity basis.