For the special orthogonal group G = SO(2n + 1) over a p-adic field, we consider a discrete series representation of a standard Levi subgroup of G. We prove that the Arthur R-group and the classical R-group of $\pi$ are isomorphic. If $\pi$ is generic, we consider the Aubert involution $\hat{\pi}$. Under the assumption that $\hat{\pi}$ is unitary, we prove that the Arthur R-group of $\hat{\pi}$ is isomorphic to the R-group of $\hat{\pi}$ defined by Ban (Ann. Sci. École Norm. Sup. 35 (2002), 673–693; J. Algebra 271 (2004), 749–767). This is done by establishing the connection between the A-parameters of $\pi$ and $\hat{\pi}$. We prove that the A-parameter of $\hat{\pi}$ is obtained from the A-parameter of $\pi$ by interchanging the two $\textit{SL}(2,\mathbb{C})$ components.