How to implement Chromecast in reverse?

Question

DLNA

Is it possible to make Chromecast (and analogues, Ezcast) work backwards by setting / flashing: receive an HDMI signal at the input and broadcast it via WIFI (dlna, miracast)?
The task is to connect a video signal source (set-top box, multimedia player, etc.) to a projector without video inputs (only wireless, on android).
I know that there are similar HDMI converters / extenders, but they are very expensive, they are sold in pairs (receiver / transmitter), etc other...