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This paper focuses on the downlink of a cellular system and studies opportunistic multiuser scheduling under imperfect channel state information, by exploiting the memory inherent in the channel. The channel between the base station and each user is modeled by a two-state Markov chain and the scheduled user sends back an ARQ feedback that arrives at the scheduler with a random delay, i.i.d. across users and time. The scheduler indirectly estimates the channel via accumulated delayed-ARQ feedback and uses this information to make scheduling decisions. The throughput maximization problem is formulated as a partially observable Markov decision process (POMDP). For the case of two users in the system, it is shown that a greedy policy is sum throughput optimal for any distribution on the ARQ feedback delay. For the case of more than two users, the greedy policy is suboptimal and numerical studies demonstrate that it has near optimal performance. Also, the greedy policy can be implemented by a simple algorithm that does not require the statistics of the underlying Markov channel or the ARQ feedback delay, thus making it robust against errors in system parameter estimation. Establishing an equivalence between the two-user system and a genie-aided system, a simple closed form expression for the sum capacity of the downlink is obtained. Further, inner and outer bounds on the capacity region of the downlink are obtained.