Value methods for solving stochastic games with partial observability model the uncertainty of the players as a probability distribution over possible states, where the dimension of the belief space is the number of states. For many practical problems, there are exponentially many states which causes scalability problems. We propose an abstraction technique that addresses this curse of dimensionality by projecting the high-dimensional beliefs onto characteristic vectors of significantly lower dimension (e.g., marginal probabilities). Our main contributions are (1) a novel compact representation of the uncertainty in partially observable stochastic games and (2) a novel algorithm using this representation that is based on existing state-of-the-art algorithms for solving stochastic games with partial observability. Experimental evaluation confirms that the new algorithm using the compact representation dramatically increases scalability compared to the state of the art.