This work focuses on the half-duplex (HD) relaying based on the generalized quantize-and-forward (GQF) scheme in the slow fading Multiple Access Relay Channel (MARC) where the relay has no channel state information (CSI) of the relay-to-destination link. Relay listens to the channel in the first slot of the transmission block and cooperatively transmits to the destination in the second slot. In order to investigate the performance of the GQF, the following steps have been taken: 1)The GQF scheme is applied to establish the achievable rate regions of the discrete memoryless half-duplex MARC and the corresponding additive white Gaussian noise channel. This scheme is developed based on the generalization of the Quantize-and-Forward (QF) scheme and single block with two slots coding structure. 2) as the general performance measure of the slow fading channel, the common outage probability and the expected sum rate (total throughput) of the GQF scheme have been characterized. The numerical examples show that when the relay has no access to the CSI of the relay-destination link, the GQF scheme outperforms other relaying schemes, e.g., classic compress-and-forward (CF), decode-and-forward (DF) and amplify-and-forward (AF). 3) for a MAC channel with heterogeneous user channels and quality-of-service (QoS) requirements, individual outage probability and total throughput of the GQF scheme are also obtained and shown to outperform the classic CF scheme.