If you try to insert html tags in K2 title fields (the fields when you try to create a category or an item) the html will be stripped from the title after saving. Because of this, you can't style certain parts of the title.

How can I edit K2 that it doesn't strip html tags from title fields?

im working on something similar
my idea is to do it in the override like this
in the override
explode the title string into array of words using " " qualifier
loop thru array
echo out styling around first word and not the rest to rebuild the string with formatting

I think I get what you mean, but I don't know how to do it. It would be easier to just allow html tags in the title. Currently there is a function present that checks if there are html tags in titles and strippes them from the title when found. So if we can delete this function this problem should be resolved. The question is where is this function? Seeing that Joomla's com_content has this issue as well, K2 may have inherited it.

There are also some settings about which tags get stripped i think, but haven't been there in a while.
I usually have quicker results with overrides and css4k2 as i can use the core of both joomla and k2 without delaying until new versions are released which may or may not be incorporated.
I read a post the other day from Akeeba support that said " he recommended a fix, but it was not incorporated into j core" therefore he is limited to what he can do.

Somewhere in joomla's core files there should be a line that contains "strip" and then some unwanted characters. I'm sure I can figure it out if I find the correct file.
Sadly this here is for Joomla 1.0: forum.joomla.org/viewtopic.php?p=154925

I will keep you updated if I have succeeded.

It seems to me, like K2 would use for title cleaning Joomlas own stripping method, taken from library/joomla/filter/output.php.
Look into line 62 in administrator\components\com_k2\tables/k2item.php you will see