Hey there Martin,
It sounds like you would like to use your Google account in the calendar application. You can set that account up in your System Preferences, using the Internet Accounts pane:
Quickly set up your Internet accounts from Google, LinkedIn, Yahoo!, and other providers for multiple Mac apps, such as Mail, Contacts, Calendar, Notes, Reminders, and Messages.
List of accounts (on the left)
Shows the accounts already set up on your Mac. Select an account to see its features and settings.
List of account features or list of account types (on the right)
If an account is highlighted on the left, its features and settings are listed on the right. Select the features you want to use and change settings as you like.
If no account is highlighted on the left, you can add one by clicking a provider such as iCloud on the right.
To add an account, click Add (+), then in the list that appears on the right, click an account provider. You can also click Add Other Account to add an account of a type not listed on the right, such as a server on your network.
If you don’t have an account you want to add, create one on the provider’s website or request one from your network administrator.
To remove the highlighted account and turn off all its features, click Delete (–).
If you remove an account while your Mac is set up for iCloud Keychain, the account is also removed from your other Mac computers set up for iCloud Keychain.
If you already have another account setup and using the Calendars application, you can set your Google account as the default one in the Messages Preferences:
Thank you for using Apple Support Communities.
All the very best,