Hi, does one experience the same problem? When I send an invitation for a new game I do not see the new game in my list, nor does my opponent.

It's not a new game until your opponent accepts. Your opponent should see a new invitation. I don't know where those show up in the redesigned site, but I'm sure it's not as a game.

They should appear as a message for the opponent.

I'm the Tony's opponent and I don't see any invitation message in my message list.

Invitations are supposed to show up in the top-right bar.  From left to right, I see the envelope (for messages), the three cubes (# of games to move in),  a bulleted list (invitations), then my username.

I see the same

It works now. Thank you all for your comments.