Jordan decomposition and real-valued characters of finite reductive   groups with connected center
  Let $\bf{G}$ be a connected reductive group with connected center defined over $\mathbb{F}_q$, with Frobenius morphism $F$. We parameterize all of the real-valued irreducible complex characters of ${\bf G}^F$ using the Jordan decomposition of characters. 
Bhama Srinivasan and C. Ryan Vinroot
math.RT