The following step-by-step guide shows how to install Microsoft Windows 11 (latest Insider Preview build 22463.1000) on top of VirtualBox 6.1; this guide has been tested and verified on both macOS as well as Linux hosts. This is to address the reported issue that Windows 11 could not be installed as a VirtualBox VM.
NB: those instructions should be also valid for Microsoft Windows 11 Generally Available release, actually targeted for October 5, 2021.
The first step is to properly configure the virtual machine that will guest the "Microsoft Windows 11" Installation; the virtual machine has to be configured in the following way (minimum requirements), based on official "Windows 11 Specs and System Requirements" and your system needs to have proper updated x86 CPU:
When the Registry Editor opens, navigate to "HKEY_LOCAL_MACHINE\SYSTEM\Setup", right-click on the "Setup" key and select "New => Key".
When prompted to name the key, enter "LabConfig" and press enter.
Now right-click on the "LabConfig" key and select "New => DWORD (32-bit)" value and create a value named "BypassTPMCheck", and set its data to "1". With the same steps create the "BypassRAMCheck" and "BypassSecureBootCheck" values and set also their data to "1", so it looks like the following image.