The gross features of the observed baryon excitation spectrum below 2 GeV are well explained if the spectrum generating algebra of its intrinsic orbital angular momentum states is o(4) ⊗ su(2)_I. The spins of the resonances are obtained through the coupling of a Lorentz bi-spinor {1/2,0} ⊕ {0,1/2} to a multiplet of the type {j,j} in its O(4)/O(3) reduction. The parities of the resonances follow from those of the O(3) members of the {j,j} multiplets. In this way relativistic SL(2,C) representations are constructed. For example, the first S₁₁, P₁₁, and D₁₃ states with masses around 1500 MeV fit into the {1/2,1/2} ⊗ [{1/2,0} ⊕ {0,1/2}] representation. The observed parities of the resonances correspond to natural parities of the {1/2,1/2} states. The second P₁₁, S₁₁, D₁₃ — together with the first P₁₃, F₁₅, D₁₅, and (a predicted) F₁₇-resonances, centered around 1700 MeV, are organized into the {3/2,3/2} ⊗ [{1/2,0} ⊕ {0,1/2}] representation. We argue that the members of the {3/2,3/2} multiplet carry unnatural parities and that in this region chiral symmetry is restored. In the N(939)→ N(1650) transition the chiral symmetry mode is changed, and therefore, a chiral phase transition is predicted to take place.