Is there a hash function $H$ and operation $\otimes$, which fulfill the following property?
$$ H(A) \otimes H(B) = H(A \otimes B) $$
$A$ and $B$ are two byte blocks of identical length, if necessary restricted to a fixed length (e.g. 128 bytes). $H$ should be a cryptographic hash function, in particular, it should be pre-image and collision resistant.
One idea based on a system of equations using $XOR$ I asked in the mathematics forum. But I am mostly interested in existing approaches or a reasoning why this might not be possible.