As I do so that only the titles of tags chosen to appear on the homepage.
I am using the menu k2 -> tag.
When shown on the main page appears the entire article.
I would like to appear only the title of the article, how can I do?
I want only the title of the article to appear on the main page when you click on the link tag.

This should work...
Find the file tag.php in the components/com_k2/templates/default folder. Make a copy of it and save it so you have a copy of the original file (I like to name mine something like tagOLD.php) just in case you ever need to restore the original for any reason.

Open your code editor of choice and paste the following...