Can you keep google from redirecting your searches?

What do you mean by redirecting them? Do you mean, from opening up your searches in a new window?

Go to google.com. Click on the link next to the search field that's labeled "Preferences." If you scroll down, you'll see a checkbox at the bottom of the page that's labeled "Open search results in a new browser window." If that is checked, then search results will pop up in a separate window. Uncheck it if you want it to open in the same window.