I really didn't think anyone would reply to my message.
I apologize for its length. I could have described the
problem using half as many words.

I just want to thank James Sweet, Sam Goldwasser,
System Alchemist, and NSM for their responses.

Sam, I don't have any idea why more and more home
appliances are equipped with overly complex add-ons
like IR remotes, etc. I grew up totally fascinated by
anything techincal, so I guess I shouldn't complain.
Still, this obsession with adding a remote to almost
everything had definitely gone too far.

System Alchemist, your idea about adding a simple
IR repeater is probably the least complex solution to
this problem. I was thinking along the same lines
myself.

This whole thing has got me down in the dumps.
I need that stupid air purifier in my bedroom. My
allergies are so bad I can hardly sleep at night.

Maybe I'll drag myself into my home workshop or the
lab where I work and try to breadboard something that
will do the job.

Holophote