I found solution! Take a look here: http://www.tersus.com/#Id=981
html.allowHTMLTags - "Unless 'true', HTML tags are escaped in content text (<Value>). Valid for Text Display, Pane, Generic HTML Display"
So, you have to create Text Display (not Text Input), add html.allowHTMLTags property (set shared to true) and then set value to <input name="searchfield"> like this
opening up so many possibilities...
But, can we do the same using TextInput? Yes, we can :) Trick is to set <Read Only> to Yes (and html.allowHTMLTags to true as well)
For best results, use the Firefox browser..