Why doesn't the translation of the genitive in Mark 11:22 use the word of? How is theology used to translate this verse?

The Greek genitive case can be used in dozens of ways, and to leave it as simply an 'of' idea is often very misleading. For example, the genitive case is used with the comparative adjective for the idea of comparison. We would translate this something like, "His car is better THAN her car." The 'than' is the genitive word 'of.' But to translate it as 'his car is better OF her car' doesn't make any sense. In Mark 11:22, although there are a couple of valid ways to translate the text, when one is dealing with God as the object, it's difficult to think of more than one. So, yes, theology does play a part in translation, but necessarily so. There are some groups that want to translate this passage as 'Have the faith that God has' but such an idea is unparalleled anywhere else in the Bible and doesn't fit the context. 'Have faith in God' is the preferred translation and meaning.