In Sutton & Barto's Reinforcement Learning: An Introduction page 63 the authors introduce the optimal state value function in the expression of the optimal action-value function as follows: $q_{*}(s,a)=\mathbb{E}[R_{t+1}+\gamma v_{*}(S_{t+1})|S_{t}=s, A_{t}=a], \forall s \in S, \forall a \in A$.

I don't understand what $v_{*}(S_{t+1})$ could possibly mean since $v_{*}$ is a mapping, under the optimal policy $\pi_{*}$, from states to numbers which are expected returns starting from those states and at different time steps. So I don't really understand $v_{*}(S_{t+1})$.

In Sutton & Barto's Reinforcement Learning: An Introduction page 63 the authors introduce the optimal state value function in the expression of the optimal action-value function as follows: $q_{*}(s,a)=\mathbb{E}[R_{t+1}+\gamma v_{*}(S_{t+1})|S_{t}=s, A_{t}=a], \forall s \in S, \forall a \in A$.

I don't understand what $v_{*}(S_{t+1})$ could possibly mean since $v_{*}$ is a mapping, under the optimal policy $\pi_{*}$, from states to numbers which are expected returns starting from those states and at different time steps. 

I believe that the authors use the same notation to denote the state-value function $v$ that verify $v(s)=\mathbb{E}[G_{t}|S_{t}=s], \forall s \in S$ and the random variable $\mathbb{E}[G_{t+1}|S_{t+1}]$ but I'm not sure.