Cockroach reproduction typically involves the male cockroach depositing sperm packets, called spermatophores, into the female's reproductive system. This process is usually initiated when the male courts the female through various behaviors, including antennal contact and sometimes even offering a food gift.
Once the female accepts the spermatophore, it is transferred into her reproductive organs, where fertilization occurs. Female cockroaches can store sperm for an extended period and use it to fertilize their eggs as needed. This allows them to produce multiple egg cases, or oothecae, without requiring constant mating.
Cockroach reproduction is quite fascinating from a biological perspective, but it may not be a pleasant topic for everyone. If you have any more specific questions or need additional information, please feel free to ask.