With the new Apple TV 4K, customers have reported issues with being able to transmit a full 4K signal through a receiver. It will work fine when directly connected to the TV.
The following information assumes that the rest of the HDMI chain is 4K compliant, i.e. cables, TVs, etc and everything is configured to output full 4K.
HDMI output signals have an inherent error rate. The poorer the quality of the HDMI output board, and the cheaper they are made, the greater the error rate. Modern smart TVs are allowed to have a HDMI error rate tolerance of up to 30%, meaning that if the incoming live signal has an error rate of 30% or less, the TV will still be able to output a picture. The problem arises when more than one HDMI interaction is required - the more HDMI interactions, the greater the error rate. So when an incoming HDMI signal of 30% is passed through an intermediary device, which has it's own error rate (even if it's as low as 1%), this will exceed the tolerance of the smart TV, resulting in an inconsistent or lack of picture.
Solution - a potential solution is to boost the incoming HDMI signal, by placing some sort of HDMI booster/buffer in between the Apple TV 4K's output and the first HDMI interaction. This should theoretically recode the incoming HDMI signal and reduce the error to a level that may be more manageable. Another potential solution is to use a quality HDMI splitter, which will do a similar boost but may also result in a boosted error rate.